Math12 Pre-Calc Review - Trig

Transcription

1 Math1 Pre-Calc Review - Trig Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following angles, in degrees, is coterminal with, but not equal to, 6 5 π radians? A. 96 C. 86 B. 576 D. 16. Which graph represents an angle in standard position with a measure of 5 8 π rad? A. C. B. D. 1

2 . Which function, where x is in radians, is represented by the graph shown below? A. y = cos x C. y = cos x B. y = sin x D. y = sin x. Determine the exact value of cos 15. A. C. B. D Completion Complete each statement. 1. For the function y = a cosb( x c) + d, d affects the of the graph. Ê. The period of the function y = 8sin π ( x 9) ˆ is. Ê. The phase shift of the function y = 8sin π 1 ( x 7) ˆ + is unit(s) to the.. The general solution, in degrees, for the equation cos x 1 = 0 is.

3 Short Answer 1. π radians is equal to how many degrees?. The exact radian measure for an angle of 55 is. What are the possible values of θ, to the nearest hundredth of a radian, when cos θ = 0.58?. If the angle θ is 1600 in standard position, in which quadrant does it terminate? 5. The period (in degrees) of the graph of y = cos x is 6. The amplitude and period (in degrees) of y = sin 5x are Ê Ê 7. What is the amplitude of the sinusoidal function y = 7sin 8 x π ˆˆ 5? Ê Ê 8. What is the period of the sinusoidal function y = cos 8 x π ˆˆ? Ê Ê 9. Determine the phase shift of the sinusoidal function y = 6sin 5 x π ˆˆ +.

4 10. Give an equation for a transformed sine function with an amplitude of 5 8, a period of 5, a phase shift of rad to the right, and a vertical translation of 9 units down. 11. What are the solutions for sin x 1 = 0 in the interval 0 x 60? 1. Describe the transformations that, when applied to the graph of y = cos x, result in the graph of È y = cos 1 Ê 8 x π ˆ ÎÍ Determine the exact measures for all angles where tanθ = in the domain 180 θ What is the solution for cos x = 0 for 0 x π?

5 ID: A Math1 Pre-Calc Review - Trig Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Average OBJ: Section.1 NAT: T1 TOP: Angles and Angle Measure KEY: radians degrees. ANS: B PTS: 1 DIF: Easy OBJ: Section.1 NAT: T1 TOP: Angles and Angle Measure KEY: radians. ANS: A PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: T KEY: graph sinusoidal function. ANS: D PTS: 1 DIF: Average OBJ: Section 6. NAT: T6 TOP: Sum, Difference, and Double-Angle Identities KEY: difference identities COMPLETION 1. ANS: vertical displacement PTS: 1 DIF: Easy OBJ: Section 5.1 Section 5. NAT: T Transformations of Sinusoidal Functions KEY: amplitude period phase shift vertical displacement sinusoidal function. ANS: 6 KEY: period sinusoidal function. ANS: 7, right KEY: phase shift sinusoidal function. ANS: n and n, where n I PTS: 1 DIF: Average OBJ: Section 6. NAT: T6 TOP: Solving Trigonometric Equations Using Identities KEY: general solutions SHORT ANSWER 1. ANS: 0 PTS: 1 DIF: Easy OBJ: Section.1 NAT: T1 TOP: Angles and Angle Measure KEY: radians degrees 1

6 ID: A. ANS: 17 1 π PTS: 1 DIF: Easy OBJ: Section.1 NAT: T1 TOP: Angles and Angle Measure KEY: radians degrees. ANS:.19 PTS: 1 DIF: Average OBJ: Section. NAT: T TOP: Introduction to Trigonometric Equations KEY: reciprocal trigonometric ratios approximate values. ANS: quadrant II PTS: 1 DIF: Average OBJ: Section.1 NAT: T1 TOP: Angles and Angle Measure KEY: rotations standard position 5. ANS: 90 PTS: 1 DIF: Easy OBJ: Section 5.1 NAT: T KEY: period sinusoidal function 6. ANS: amplitude = period = 7 PTS: 1 DIF: Average OBJ: Section 5.1 NAT: T KEY: amplitude period sinusoidal function 7. ANS: 7 KEY: amplitude sinusoidal function 8. ANS: 1 π KEY: period sinusoidal function 9. ANS: π units to the right KEY: phase shift sinusoidal function

7 ID: A 10. ANS: y = 5 8 sin 5 π( x / ) 9 PTS: 1 DIF: Difficult OBJ: Section 5. NAT: T KEY: transformations equation properties sinusoidal function 11. ANS: x = 5 and 5 and 15 and 15 PTS: 1 DIF: Difficult + OBJ: Section 5. NAT: T TOP: Equations and Graphs of Trigonometric Functions KEY: quadratic trigonometric equation 1. ANS: a reflection in the x-axis, a vertical stretch by a factor of, a horizontal stretch by a factor of 8, a phase shift of π to the right, and a vertical translation of 1 unit up KEY: transformations sinusoidal function 1. ANS: The tangent ratio is negative in quadrants II and IV. In quadrant II for the domain 0 θ 180, θ = 10. In quadrant IV for the domain 180 θ 0, θ = 60. PTS: 1 DIF: Difficult OBJ: Section. NAT: T TOP: Trigonometric Ratios KEY: primary trigonometric ratios exact value 1. ANS: cos x = 0 cos x = cos x = Ê ˆ x = cos 1 = π 6 Since cosine is also positive in quadrant IV, another solution is π π 6 = 11π 6. PTS: 1 DIF: Easy OBJ: Section 6. NAT: T6 TOP: Solving Trigonometric Equations Using Identities KEY: exact value