Math 4 Snow Day. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Size: px

Start display at page:

Download "Math 4 Snow Day. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question."

Sybil Hines
5 years ago
Views:

1 Class: Date: Math 4 Snow Day Multiple Choice Identify the choice that best completes the statement or answers the question.. Simplify the rational expression x x x x x x 0. x x. Which function has an amplitude of and a period of? f x cos x f x cos x f x cos x f x cos x. Simplify the rational expression x x x x x 9. x x x x x x 4. Which is the equation of the graph shown below? f x sinx f x sinx f x sinx f x sin x

2 . If sin 0.788, what is the approximate value of cos 8? Use a special right triangle to write tan 0 as a fraction. 7. What is the equation for the graph shown below? y 4sin x 8 y cos x 4 y sin x 4 e. y sin x y 4cos x 8 8. In the figure below, ABC DEF. Find the ratio EF DF. 4 4

3 9. Which function has an amplitude of and a period of? y sin 4x y cos 4x y sin x y cos x 0. What is the exact value of sin. In right triangle ABC, A and B are acute angles. If sin A =, which of the following statements is true? cos B = cos B =. What is the exact value of cos? cos B = cos B =. Convert radians to degrees Which function has an amplitude of and a period of? f x cos x f x cos x f x cos x f x cos x. Find sin F and sin G. sin F 0.8, sin G 0.9 sin F.04, sin G.7 sin F.7, sin G.04 sin F 0.9, sin G 0.8

4 . Simplify x x 0 x x x x x x 9. x x x x x 8x x 7x 0 x x x x 7. In which two quadrants is sin x negative? Quadrants I and II Quadrants II and IV Quadrants II and III Quadrants III and IV 8. What is the value of A if sin A? Not here 9. The coordinates of a point on the unit circle are,. What standard position angle, in the interval [0,), corresponds to this point? Write the trigonometric ratio for cos X as a fraction and as a decimal, rounded if necessary to the nearest hundredth. cos X = 9. cos X = 0.8 cos X = 9 0. cos X = An arc on the unit circle is 4 units long. What is the degree measure of the arc s central angle?

5 . Multiply x 4x 8 x 9 x 4 x 4 x x (x 4) 4(x 4). Simplify your answer.. Given that sin , which statement below is also true? (x )(x ) (x 4)(x x ) cos sin cos cos Convert radians to degrees The graph of which function is shown? y cosx y sinx y sinx e. y sinx y sinx. Which angle has a cosine of? A B

6 7. Subtract. Simplify your answer. x x x 8x x 4x x 8x x x x x 8x x x x 8x x x x x 8x x 8. Which expression is equivalent to the rational expression x y xy x y x y 9. Choose the statement that is true about the given quantities. Column A Column B sin 4 cos 4 (where x 0 and y 0)? xy x y The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the given information. 0. The legs of a right triangle measure.4 meters and. meters. To the nearest tenth, what is the measure of the smallest angle? What is the exact value of tan 4?. Use the triangle below to find cos V

7 . What is tan K? What is sin 49 to the nearest tenth? What is tan4 to the nearest hundredth? In which two quadrants is tan x positive? Quadrants I and II Quadrants II and IV Quadrants I and III Quadrants III and IV 7. Which has the same value as sin cos cos sin sin 8. How do you find the value of sin for a given value of (0 ) using the unit circle? The angle of rotation in standard position traverses an arc on the unit circle. The x-coordinate of the arc s endpoint that lies on the terminal side of is the value of sin. The angle of rotation in standard position traverses an arc on the unit circle. The y-coordinate of the arc s endpoint that lies on the terminal side of is the value of sin. The angle of rotation in standard position traverses an arc on the unit circle. The ratio of the x-coordinate to the y-coordinate of the arc s endpoint that lies on the terminal side of is the value of sin. The angle of rotation in standard position traverses an arc on the unit circle. The ratio of the y-coordinate to the x-coordinate of the arc s endpoint that lies on the terminal side of is the value of sin. 7

8 9. If A and B are complementary angles and cos A = 0.09, which of the following statements is true? sin B = 0.09 sin B = 0.94 cos B = 0.09 There is not enough information to determine whether any of the statements are true. 40. An arc on the unit circle is 4 units long. What is the radian measure of the arc s central angle? 4 radian 4 radians radians 4 radian 4. What trigonometric ratio is defined as opposite leg adjacent leg? cosine sine hypotenuse tangent 4. The legs of a right triangle measure 4 and. To the nearest tenth of a degree, what is the measure of the angle opposite the shortest side? Convert 0 to radians. radians radians radians radians 44. To the nearest thousandth, what is tan77? What is the exact value of sin 4? 8

9 4. In the figure below, GHI JKL. Find the ratio HI GH. 47. Simplify the rational expression r 8r. Identify any excluded values. r r r; r or 0 r; no excluded values r r r ; r or 0 r; r 48. Ad Simplify your answer. x 8 x 4 x x 4 x Find tan A and tan B. x 4 x 4 x tan A 0.8, tan B. tan A.08, tan B 0.4 tan A., tan B 0.8 tan A 0.9, tan B.4 9

0. Which function is graphed? y cos x y cos x y cos x y cos x. In which two quadrants is cos x negative? Quadrants I and IV Quadrants II and IV Quadrants II and III Quadrants III and IV.

10 0. Which function is graphed? y cos x y cos x y cos x y cos x. In which two quadrants is cos x negative? Quadrants I and IV Quadrants II and IV Quadrants II and III Quadrants III and IV. Given that cos 7 0.9, which statement below is also true? sin 0.9 sin sin 0.9 cos 0.9. Find the cosine of R as a decimal Simplify x x x. x 4 x 4 x 4 x 4. Which function has an amplitude of and a period of? f x cos 4x f x 4cos x f x cos x f x cos x 0

11 . What is the exact value of sin? x 8 7. Simplify x 4 x x. x 9 x x x x x x 8. The graph of which function has a period of and an amplitude of? y sinx y sinx y sin x y sin x 9. What is the reference angle corresponding to 7 4? Which angle measure is shown in the diagram? 4 radians 4 radians 4 radians e. 4 radians 4 radians

12 Math 4 Snow Day Answer Section MULTIPLE CHOICE. ANS: D PTS: REF: ef4fa-48-df-9c7d-008f0dea OBJ: Simplifying Rational Expressions with Trinomials NAT: NT.CCSS.MTH.0.9-.A.APR. STA: MCC9-.A.APR. LOC: MTH.C TOP: Simplifying Rational Expressions KEY: rational expression DOK: DOK. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: A PTS: REF: fc0a-48-df-9c7d-008f0dea OBJ: Simplifying Rational Expressions Using Opposite Binomials NAT: NT.CCSS.MTH.0.9-.A.APR. STA: MCC9-.A.APR. LOC: MTH.C TOP: Simplifying Rational Expressions KEY: rational expression DOK: DOK 4. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: D The sine of an acute angle is equal to the cosine of its complement. Thus, cos A B Feedback Recall that the sine of an acute angle is equal to the cosine of its complement. Recall that the sine of an acute angle is equal to the cosine of its complement. C You found cos, not cos 8. D That s correct! PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: right triangle complementary angles trigonometric ratios sine cosine DOK: DOK. ANS: A PTS: REF: bcc-48-df-9c7d-008f0dea OBJ: Finding Trigonometric Ratios in Special Right Triangles NAT: NT.CCSS.MTH.0.9-.F.TF. NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.F.TF. LOC: MTH.C MTH.C TOP: Trigonometric Ratios KEY: trigonometric ratio trigonometry tangent special right triangles DOK: DOK 7. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. NT.CCSS.MTH.0.9-.F.BF. STA: MCC9-.F.TF. DOK: DOK

13 8. ANS: C Since ABC DEF, EF DF is equivalent to BC AC, or. Feedback A You chose the ratio DF EF, not EF DF. B Corresponding sides in similar triangles are proportional. Decide which sides in ABC correspond to EF and DF in DEF. C That s correct! D Corresponding sides in similar triangles are proportional. Decide which sides in ABC correspond to EF and DF in DEF. PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. KEY: similar triangles trigonometric ratios DOK: DOK 9. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK 0. ANS: B PTS: REF: A..EN.ST.0 NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: trigonometric functions DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: cofunctions DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: define evaluate radians unit circle DOK: DOK. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK 4. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.A.APR.7 STA: MCC9-.A.APR.7 DOK: DOK 7. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.F.TF.4 STA: MCC9-.F.TF.4 KEY: even/odd identify patterns DOK: DOK 8. ANS: C PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 9. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: define evaluate radians unit circle DOK: DOK 0. ANS: C PTS: REF: bc0c0a-48-df-9c7d-008f0dea OBJ: Finding Trigonometric Ratios NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. LOC: MTH.C MTH.C TOP: Trigonometric Ratios KEY: trigonometric ratio trigonometry cosine DOK: DOK

14 . ANS: C If a central angle in the unit circle intercepts an arc of length s, then the angle s radian measure is s. So, the measure of the central angle that intercepts the given arc is The measure of the arc s central angle is 40. radians. Convert the measure to degrees. A B C D Feedback If a central angle in the unit circle intercepts an arc of length s, then the angle s radian measure is s. If a central angle in the unit circle intercepts an arc of length s, then the angle s radian measure is s. That s correct! If a central angle in the unit circle intercepts an arc of length s, then the angle s radian measure is s. PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: radians arc length unit circle degrees DOK: DOK. ANS: A PTS: REF: ae0c-48-df-9c7d-008f0dea NAT: NT.CCSS.MTH.0.9-.A.APR.7 STA: MCC9-.A.APR.7 LOC: MTH.C TOP: Multiplying and Dividing Rational Expressions KEY: rational expression multiply divide DOK: DOK. ANS: D The sine of an angle is equal to the cosine of its complement. Thus, cos A B C D Feedback Recall that the sine of an acute angle is equal to the cosine of its complement. The sine of an acute angle is not the same as the sine of its complement unless the angle is 4. Recall that the sine of an acute angle is equal to the cosine of its complement. That s correct! PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: right triangle complementary angles trigonometric ratios sine cosine DOK: DOK 4. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: E PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK

15 7. ANS: B PTS: REF: d4-48-df-9c7d-008f0dea OBJ: Subtracting Rational Expressions with Like Denominators NAT: NT.CCSS.MTH.0.9-.A.APR.7 STA: MCC9-.A.APR.7 LOC: MTH.C TOP: Adding and Subtracting Rational Expressions KEY: rational expression add like denominators DOK: DOK 8. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.A.APR. STA: MCC9-.A.APR. KEY: rewrite rational expressions DOK: DOK 9. ANS: C PTS: REF: G.07.EN.ST.09 NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: sine and cosine ratios DOK: DOK 0. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: define evaluate radians unit circle DOK: DOK. ANS: A UV 9 by the Pythagorean Theorem; cos V A Feedback That s correct! B You found sin V, not cos V. C You found tan V, not cos V. D Recall that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, not the ratio of the hypotenuse to the adjacent side. PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. KEY: right triangles cosine ratio DOK: DOK. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 4. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK. ANS: C PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK. ANS: C PTS: NAT: NT.CCSS.MTH.0.9-.F.TF.4 STA: MCC9-.F.TF.4 KEY: even/odd identify patterns DOK: DOK 7. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: trigonometric functions DOK: DOK 4

16 8. ANS: B The angle of rotation in standard position traverses an arc on the unit circle. The arc ends at a point (x, y) on the terminal side of. The unit circle definitions for the trigonometric functions are sin y, cos x, and tan y x. So, the y-coordinate of the arc s endpoint that lies on the terminal side of is the value of sin. A B C D Feedback The x-coordinate of the arc s endpoint that lies on the terminal side of is the value of cos. That s correct! The ratio of the x-coordinate to the y-coordinate of the arc s endpoint that lies on the terminal side of is the value of cot. The ratio of the y-coordinate to the x-coordinate of the arc s endpoint that lies on the terminal side of is the value of tan. PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: sine radians unit circle DOK: DOK 9. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: cofunctions DOK: DOK 40. ANS: B If a central angle in the unit circle intercepts an arc of length s, then the angle s radian measure is s. So, the measure of the central angle that intercepts the given arc is 4 radians. A B C D Feedback 4 radian is the measure of the central angle of an arc that is unit long. 4 That s correct! radians is the measure of the central angle of an arc that is units long. 4 radian is the measure of the central angle of an arc that is unit long. 4 PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: radians arc length unit circle DOK: DOK 4. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 4. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 4. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK 44. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 4. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: evaluate unit circle DOK: DOK

17 4. ANS: D Since GHI JKL, HI GH KL is equivalent to, or JK. Feedback A You chose the ratio GH HI, not HI GH. B Corresponding sides in similar triangles are proportional. Decide which sides in JKL correspond to HI and GH in GHI. C Corresponding sides in similar triangles are proportional. Decide which sides in JKL D correspond to HI and GH in That s correct! GHI. PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. KEY: similar triangles trigonometric ratios DOK: DOK 47. ANS: A PTS: REF: c99e-48-df-9c7d-008f0dea OBJ: Simplifying Rational Expressions NAT: NT.CCSS.MTH.0.9-.A.APR. STA: MCC9-.A.APR. LOC: MTH.C TOP: Simplifying Rational Expressions KEY: rational expression DOK: DOK 48. ANS: A PTS: REF: b07d-48-df-9c7d-008f0dea OBJ: Adding Rational Expressions with Like Denominators NAT: NT.CCSS.MTH.0.9-.A.APR.7 STA: MCC9-.A.APR.7 LOC: MTH.C TOP: Adding and Subtracting Rational Expressions KEY: rational expression add like denominators DOK: DOK 49. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 0. ANS: B PTS: REF: A.4.EN.ST.0 NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: trigonometric graphs DOK: DOK. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF.4 STA: MCC9-.F.TF.4 KEY: even/odd identify patterns DOK: DOK. ANS: A The sine of an angle is equal to the cosine of its complement. Thus, sin 0.9. A B C D Feedback That s correct! Recall that the sine of an acute angle is equal to the cosine of its complement. Recall that the sine of an acute angle is equal to the cosine of its complement. The cosine of an acute angle is not the same as the cosine of its complement unless the angle is 4. PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT.7 STA: MCC9-.G.SRT.7 KEY: right triangle complementary angles trigonometric ratios sine cosine DOK: DOK

18 . ANS: C PTS: NAT: NT.CCSS.MTH.0.9-.G.SRT. STA: MCC9-.G.SRT. DOK: DOK 4. ANS: D PTS: NAT: NT.CCSS.MTH.0.9-.A.APR. STA: MCC9-.A.APR. DOK: DOK. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: define evaluate radians unit circle DOK: DOK 7. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.A.APR.7 STA: MCC9-.A.APR.7 DOK: DOK 8. ANS: B PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK 9. ANS: C PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. KEY: define evaluate radians unit circle DOK: DOK 0. ANS: A PTS: NAT: NT.CCSS.MTH.0.9-.F.TF. STA: MCC9-.F.TF. DOK: DOK 7

A trigonometric ratio is a,

A trigonometric ratio is a, ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric