Trigonometry I. Exam 0

Transcription

1 Trigonometry I Trigonometry Copyright I Standards 006, Test Barry Practice Mabillard. Exam 0

2 1. The minimum and the maximum of a trigonometric function are shown in the diagram. a) Write a cosine equation for the function b) Determine the value of the y intercept, correct to three decimal places. Convert 11 to degrees 18 Trigonometry I Standards Test Practice Exam 1

3 1. Find the exact value of sinθ if cosθ =, and the terminal arm is in Quadrant I. 7. What is the period in the function f ( x) ( x) = sin 5 5. Given the point (-, -), determine the exact values of cosθ and sinθ 6. The length of arc swept out by an angle θ is 50 cm. If the radius of the circle is 18 cm, determine the measure of θ in radians. Trigonometry I Standards Test Practice Exam

4 7. Determine a value for x that would make the function f ( x) = cscx undefined in the domain [0, ) 8. Determine the value of 10 in the function f ( ) f ( x) ( x ) = sin + 9. The graph of y = 6cos x+ + 1 is illustrated below. Determine the exact values of g, h, m & n. Trigonometry I Standards Test Practice Exam

5 10. If the measure of the central angle is, determine the measures of the other two angles within the triangle. 11. Determine the number of radians between the hour hand and the minute hand at 7:00. Trigonometry I Standards Test Practice Exam

6 7 1. Determine the value of cos 1. The circle x + y = 1 is drawn below, along with the line Determine the coordinates of the two intersection points. y =. 1. The graph of f ( x) = 6sin x+dtouches the x-axis once (but does not pass through) on the interval 0 x. A possible value for d is: Trigonometry I Standards Test Practice Exam 5

7 15. a) Graph y = cos x b) Graph y = cos 1 x 1 c) State the domain of f ( x) 16. The maximum point on a trigonometric graph is at the point (-, 6), and the minimum point is at (, -). If the graph is of the form y = acos b( x+ c) + d, then determine possible values for each of the parameters. Trigonometry I Standards Test Practice Exam 6

8 17. An angle of 15 is equivalent to radians. (exact value) 18. The exact value of 1 5 cos cos 6 is 19. Write the general equation of a vertical asymptote in the graph of y = csc x 0. If cscθ = and tanθ < 0, determine the value of cosθ Trigonometry I Standards Test Practice Exam 7

9 1. Given the function f ( x) = sin ( x ) a) Sketch the graph b) Sketch y = f ( x). If the coordinates of a point P( θ ) on the unit circle is (a, b), then the coordinates of the point P θ o are Trigonometry I Standards Test Practice Exam 8

10 . State the period of the graph of y = cscθ. Convert to degrees. Express answer to one decimal place Given the function f ( x) = tan x a) Sketch y = f ( x) on the domain, b) State the domain of f ( x ) 1 c) Sketch the graph of f ( x) Trigonometry I Standards Test Practice Exam 9

11 6. A floating ball in a lake goes up and down with the tide. At 1 second, the ball has a minimum height of 5 cm below surface level. At seconds, the ball has a maximum height of 5 cm above surface level. a) Sketch a graph for the first seconds of motion b) Write an equation for the function 7. If the product of cos x and sin x is negative, then which quadrant is the angle in? 8. The value of sin is The exact value of sin cos is Trigonometry I Standards Test Practice Exam 10

12 0. If the coordinates of a point P( θ ) on the unit circle are coordinates of the point P θ o are 1,, then the 1. A tire rolls metres while turning 0. Determine the area of the wheel. Trigonometry I Standards Test Practice Exam 11

13 MULTIPLE CHOICE SECTION 1. Given a) b) c) d) 5 5 ± ± 5 cscθ =, the exact value of tanθ is. A tire has a radius of 5 m. The tire is rolled and travels a total distance of 8 m. By the time the tire stops, it has rolled through an angle of a) 8 b) 10 c) 8 rad 5 d) Given the trigonometric function f ( x ) = cos x, the statement which is true is a) f ( x) = f ( x ) b) f ( x) = f ( x) c) 1 f ( x) = f ( x) d) f ( x) = f ( x) 0 0. If 90 < θ < 180, a true statement is 0 0 a) 0 < θ < 90 b) cosθ tanθ c) 0< sinθ < 1 d) 0< cosθ < 1 Trigonometry I Standards Test Practice Exam 1

14 = 1, 5. Given the function f ( x ) = 1 cos ( x ), and the transformation g( x) f ( x) then the amplitude of a) b) c) d) 1 g( x) is 6. The function f ( x ) = secx a) (, ) b) (, ] [, ) c) 1 1,, d) ( ) has a range of 7. A wheel turns through an angle of 16 radians. This angle measurement in degrees is 0 a) b) 0 c) d) 8. A sine function has a range of [-6, ] and a period of. A trigonometric equation with these properties is a) y = 8sin θ + y = sin θ b) ( ) c) y = sin θ d) y = sin θ Trigonometry I Standards Test Practice Exam 1

15 9. The angle is co-terminal to an angle of a) 0 b) c) 5 6 d) The exact value of a) b) c) d) 7 csc is 11. Given that a) I b) II c) III d) IV cosθ = and 5 sinθ =, then the terminal arm is located in quadrant 5 1. The period of the function g(x) is 8. If g ( 0) = 1, g( ) = 6, and g( 8) = 1, then the value of g ( 1) is a) 0 b) 6 c) 1 d) 18 Trigonometry I Standards Test Practice Exam 1

16 1. An angle of on the unit circle has coordinates of a) b) 1,, c) (0, -1) d) (-1, 0) 1. If secθ > 0 and sinθ < 0, then θ terminates in quadrant a) I b) II c) III d) IV 15. The period and phase shift for the trigonometric equation a) b) c) d) period = ; phase shift = left period = ; phase shift = right period = ; phase shift = left period = ; phase shift = right 1 y = sin θ are 16. The equation of an asymptote on the graph of y = csc x is a) x = b) x = c) x = d) x = Trigonometry I Standards Test Practice Exam 15

17 17. If tan xsin x< 0, then x terminates in quadrants a) II or III b) II or IV c) I or IV d) III or IV 18. The value of a) b) 5 c) d) 11 6 sin 1 is: Trigonometry I Standards Test Practice Exam 16