Download Trig Test Review 2017

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Trig Identities and Equations Test #2 Review
All questions are calculator inactive, unless otherwise noted.
1. If sin A 
4
and A is an obtuse angle, find cos A , tan A , cos 2 A , and sin 2 A .
5
2. If cos A 
1
, and A is an acute angle, find sin A , tan A , cos 2 A , and sin 2 A .
3
3. sin 2x  sin x  0 , 0  x  2
4. cos 2x  sin x  0 , 0  x  2
5. Express 2 cos 3x sin 3x in terms of
sine only.
6. sin 2 x  3 cos 2 x , 0  x  360
7. sin 8x cos 3x – cos 8x sin 3x
8. sin(105o)
9.
10. If cosA = 1/3, find the value of cos(2A).
11. 4cosαsinα
12. cos22A – sin22A
13. Evaluate:
14. Solve the equation 3 sin2x = cos2x, for 0 ≤ x ≤ π
15. Calculator active: Solve the equation 3 cos x = 5 sin x, for x in the interval 0° ≤ x ≤ 360°,
giving your answers to the nearest degree.
16. (a) Express 2 cos2 x + sin x in terms of sin x only.
(b)
Solve the equation 2 cos2 x + sin x = 2 for x in the interval 0 ≤ x ≤ π, giving your
answers exactly.
17. Consider the trigonometric equation 2 sin2 x = 1 + cos x.
(a)
Write this equation in the form f(x) = 0, where f(x) = a cos2 x + b cos x + c,
and a, b, c ϵ .
(b)
Factorize f(x).
(c)
Solve f(x) = 0 for 0° ≤ x ≤ 360°.
18. Consider y = sin  x    .
9

(a)
(b)
The graph of y intersects the x-axis at point A. Find the x-coordinate of A, where
0 ≤ x ≤ π.
Solve the equation sin  x    = – 1 , for 0 ≤ x ≤ 2π.
9

2
19. 2 sin 2 x  3 sin x  1  0 , 0  x  180
20. 2 sin x cos x  3 cos x  0 , 0  x  2
21. 2 sin 2 x  1  0 , 0  x  2
22. cos 3 x  
3
, 0  x  90
2