Title Trigonometry Units 1-3 Final Assessment - Solutions.pdf ✅

TRIGONOMETRY UNITS ASSESSMENT - SOLUTIONS TRIGONOMETRIC FUNCTIONS 1. An angle drawn in standard position has a terminal ray that intersects the unit circle at the point (−0.352, 0.936) . Which of the following represents the value of the cosine of this angle? (1) −0.584 (3) 1.288 (2) 0.936 (4) −0.352 2. Which of the following angles, when drawn in standard position, would be coterminal with an angle that measures −  105 ? (1) 15 (3) 205 (2) 75 (4) 255 3. If f x x ( ) =10sin 4( ) then what is the value of f (30) (1) −10 3 (3) 20 3 (2) 5 3 (4) −5 4. Which of the following is a value of sin ( ) ? (1) 4  (3) 3 2 (2) 2  (4) 4 3 5. Which of the following is the range of the function y x = − + 5cos 3 11 ( ) ? (1) −5,11 (3) −6, 6 (2) 6,16 (4) −4, 26 (4) For an angle drawn in standard position, the cosine of the angle is defined as the x- coordinate of where its terminal ray intersects the unit circle. Therefore, the cosine of this angle is -0.352. Angles that are coterminal will be separated by integer multiples of : (4) (2) The function has range of all values from -1 to 1. The only one of these values that is in that range is . (1) (2)
6. What is the horizontal distance between any two consecutive x-values where the function below intersects its midline? (1) 2 3  (3) 3 (2) 2 3 (4) 6 7. At what value of  below is sec ( ) undefined? (1)  (3) 3 4  (2) 2 3  (4) 3 2  8. Which of the following represents the value of csc 60 ( ) in simplest radical form? (1) 2 3 3 (3) 2 3 (2) 2 (4) 3 9. For the angle  it is known that cos 0 ( )  and tan 0 ( )  . If  is drawn in standard position, in which quadrant would its terminal ray lie? (1) I (3) III (2) II (4) IV 10. If sin x a = and x is a first quadrant angle, then which of the following is a correct expression for secx ? (1) 2 1 a a − (3) 1 a (2) 2 1 a − a (4) 2 1 1− a 1 8sin 4 3 y x   = +     (3) The distance between two midline values will be half of a full period: Since , it will be undefined at any value where is equal to zero. The only value this is true for is . (4) (1) (2) (4)
TRIGONOMETRIC ALGEBRA 1. On which of the following intervals would y x = sin ( ) not be one-to-one? (1) 0 90     x (3) −     90 90 x (2) −     90 0 x (4) -180° ≤ x ≤ 0° 2. Which of the following values is not in the domain of the inverse cosine function? (1) 1 (3) 4 3 (2) 4 5 (4) 1 2 − 3. To the nearest degree, which of the following is the solution set to 3sin(A) = 1 on the interval 0 360    A ? (1) {19.47, 340.53} (3) 109 , 251   (2) 71 ,109   (4) {19.47, 160.53} 4. Which of the following equations will have no real solutions? (1) 5cos 3 0 ( x) − = (3) 6sin 1 0 ( x) + = (2) 5 sin (x) – 12 = 0 (4) 4cos 4 0 ( x) + = 5. The value of tan2 (60°) is which of the following? (1) 2 3 (3) 3 2 (2) 1 3 (4) 3 sin (A)= 1/3 Sine is positive in the 1 st and 2nd Quadrants. A = sin-1 (1/3) = 19.47° and 160.53° (4) The domain of the inverse cosine is the same as the range of cosine, which is all values from -1 to 1, inclusive. The only value that doesn’t fall in this range is choice (3). (3) (4) Choice (2) is correct sin x = 12/5 A sine function has to satisfy -1 ≤ sin(x) ≤ 1 (2) tan2 (60°) = (√3)2 = 3 (4)
6. If 5 cos 3 B = and sin 0 (B)  , then which of the following is the value of sin2 (B)? (1) 2 9 (3) 2 3 (2) 2 3 (4) 4 9 7. Which of the following is equivalent to sin (75°)cos(45°) – cos(75°)sin(45°)? (1) sin 70 ( ) (3) cos 70 ( ) (2) sin 30 ( ) (4) cos 30 ( ) 8. If cos A = 0.8 then which of the following is the value of cos 2( A) ? (1) 1.22 (3) 0.34 (2) 0.28 (4) −1.6 9. Which of the following is a solution to the equation (sin x – 5)(sin x – 1) = 0? (1) 45 (3) 270 (2) 90° (4) 360 10. The graph of the function 3 7cos 3 2 x y   = − +     is shown below. Which of the following is closest to the greatest solution to the equation 3 7cos 3 0 2   x − + =     on the interval 0 360     x ? (1) 200° (2) 240° (3) 280° (4) 340° (4) sin (A – B) = sin A ‧ cos B – cos A ‧ sin B sin (75° – 45°) = sin 75° ‧ cos 45° – cos 75° ‧ sin 45° = sin 30° (2) cos(2A) = 2 cos2 (A) – 1 = 2(0.8) 2 – 1 = 2(0.64) – 1 = 0.28 (2) sin x = 5 No solution sin x = 1 x = 90° (2) The greatest solution will correspond to the zero farthest to the right in the graph within the interval. This is clearly between 280° and 290° but closer to 280° on the graph. So, the best choice would be (3). (3)