Plane Trigonometry Test File Fall 2014

Transcription

1 Plane Trigonometry Test File Fall 2014 Test #1 1.) Fill in the blanks in the two tables with the EXACT values (no calculator) of the given trigonometric functions. The total point value for the tables is 10 points. For each box that is NOT correct you will lose 1 point. Θ sin Θ cos Θ tan Θ cot Θ sec Θ csc Θ 0 Θ sin Θ cos Θ 240 π/3 5π/6 8π/3 11π/6 7π/4 sin -1 (-2/3) 2.) Given that tan A = -5/12 and A is not in Quadrant 2, find the values of the other trigonometric functions. Give exact answers (no calculator). 3.) If cos A = k and 0 < A <, then what is cos(180 -A)? 4.) Convert the following to radian measure. a.) 24 b.) ) Convert the following to degree measure. a.) 7π/5 b.) 45 π 6.) A woman is standing on the ground looking at a billboard. The billboard is on top of a building. The woman is 40 feet away from the building. The angle of elevation of

2 the woman's line of sight to the top of the building is 67. The angle of elevation of the woman's line of sight to the top of the billboard is 76. How tall is the building? 7.) The wheel of a bicycle has diameter 24 inches. If the wheel is making 2 rev/sec, find the angular and linear velocity. 8.) a.) If a = 22.1, c = 17.5 and B = 109, find A, C, b and the area of the triangle. b.) If a = 3, b = 4 and c = 6, find A, B, C and the area of the triangle. c.) If A = 38.4, B = 54.1 and a = 14, find C, b, c and the area of the triangle. d.) If a = 8, b = 5 and A = 31, find c, B and C for any possible triangles. 9.) Two people are on the same side of a pole so that the pole and the two people are in a straight line. One person is 10 feet closer to the pole. Suppose the angle of elevation from the ground at one person s feet to the top of the pole is 35. Suppose the angle of elevation from the ground at the other person s feet to the top of the pole is 42. How tall is the pole? Test #2 1.) Fill in the blanks in the two tables with the EXACT values of the given trigonometric functions. The total point value for the tables is 10 points. For each box that is NOT correct you will lose 1 point. sin cos 0 /3 5 /6 8 /3 11 /6 7 /4 2.) Given that tan A = -5/12 and A is not in Quadrant 2, find the values of the other trigonometric functions. Give exact answers. 3.) Graph one complete period of the following functions. Label the angles at the beginning and end of a period, high and low points and asymptotes. Use radians. a.) y 1 2sin x b.) f ( x) tan 2x 3 4 c.) y = sec(x/6) 4.) Convert 24 to radian measure.

3 5.) Convert 7 /5 to degree measure. 6.) For each of the following functions, list the period, amplitude and phase shift. If the amplitude does not exist, write "DNE". a.) y = sin(2x - /3) b.) y = cot(3x) 7.) Suppose tan A = 4.5 and 0 < A < 3. What is A? 8.) Evaluate the following expressions. Give exact answers. a.) sin (sin -1 (4/9)) b.) cos (sin -1 (4/5)) c.) Cos -1 (1/2) d.) -1-2 tan Sin 7 9.) Graph y = tan -1 x Test #3 1.) Prove the following identities. a.) (sin A + cos A) 2 = 1 + sin 2A b.) sin 2Θ (tan Θ + cot Θ) = 2 c.) 3 sin 3 = 3 sin - 4 sin d.) 1- cos x sec x - 1 = 1+ cos x sec x+1 2.) Evaluate the following expressions. Give exact answers. No calculator. a.) cos Sin b.) cos 22.5 c.) Cos -1 (cos(4π/3)) d.) sin 82.5 cos ) Find all x that satisfy the following equation. Use radians. cos 2x = 1/3 4.) Find all x, with 0 x < 2π, that satisfy the following equations. Use radians. ANSWERS MUST BE EXACT, NOT APPROXIMATIONS!! No Calculator. a.) 1 + cos 2 x = sin x b.) sin x cos x = cos x c.) sin(2x) = 0 5.) Find all x that satisfy the following equation. Use radians. ANSWERS MUST BE EXACT, NOT APPROXIMATIONS!! No Calculator. cos 3x = 1/2 Test #4 1.) Let u = 2i - 3j, v = i + j and w = 3i. Find the following. a.) 2u - 3w b.) a unit vector in the same direction as u c.) u d.) u v e.) the angle between v and w

4 f.) the projection of u in the direction of v 2.) Graph r = cos (use radians) 3.) a.) Change the point (2, -2) to polar coordinates. b.) Change the point (4, 5 /6) to rectangular coordinates. 4.) Find the four 4th roots of 1 + i. 5.) If z = 3 (cos i sin 140 ), find z 5. 6.) The graph of r = 2 cos 360Θ would be a "flower" with "petal" at every point where cosine equals 1. a.) How many petals would the graph have? b.) Give the value of Θ for the first petal (Θ > 0) and two other values of Θ for petals. (use degrees) 7.) Graph r = Θ. (use radians) 8.) A plane is flying at 450 miles per hour with a heading of N 20 E (relative to the air. The wind is blowing 30 miles per hour with a heading of S 15 E. Find the actual heading and sped of the plane. Final Exam 1.) Fill in the blanks in the two tables with the EXACT values of the given trigonometric functions. The total point value for the tables is 10 points. For each box that is NOT correct you will lose 1 point. Θ sin Θ cos Θ tan Θ 0 Θ sin Θ cos Θ 240 π/3 5π/6 8π/3 11π/6 7π/4

5 3.) Given that tan A = -5/12 and A is not in Quadrant 4, find the values of the other trigonometric functions. Give exact answers. 4.) A woman is standing on the ground looking at a billboard. The billboard is on top of a building. The woman is 40 feet away from the building. The angle of elevation of the woman's line of sight to the top of the building is 67. The angle of elevation of the woman's line of sight to the top of the billboard is 76. How tall is the building? 5.) For each of the following functions, list the period and the amplitude. If the amplitude does not exist, write "DNE". a.) y = sin(2x - π/3) b.) y = - sin(2x + π) c.) y = cos(3x) 6.) Graph one complete period of the following functions. Label all of the important angles we talked about. Use radians. a.) y = sin(x - π/3) b.) y = 3-2 cos 3x - π 3 7.) Prove the following identities. a.) (sin A + cos A) 2 = 1 + sin 2A b.) sin 2Θ (tan Θ + cot Θ) = 2 c.) _ 1 _ + _ 1 _ = 2 sec 2 A 1 + sin A 1 - sin A 8.) Evaluate the following expressions. Give exact answers. a.) cos Sin b.) cos ) Find all x, with 0 x < 2π, that satisfy the following equations. Use radians. ANSWERS MUST BE EXACT, NOT APPROXIMATIONS!! a.) 1 + cos 2 x = sin x b.) sin x cos x = cos x c.) sin(2x) = 0 10.) a.) Change the point (2, -2) to polar coordinates. b.) Change the point (4, 5π/6) to rectangular coordinates. 11.) Let u = 2i - 3j, v = i + j and w = 3i. Find the following. a.) 2u - 3v b.) a unit vector in the same direction as v c.) u v d.) the angle between v and w e.) the projection of u in the direction of v f.) u