Honors Precalculus
Chapter 5
Flash Cards
1. Evaluate without using a calculator.
Find sinθ and cosθ if tanθ =
3
and sinθ <0.
4
2.Use basic identities to simplify the expression. 3.Use basic identities to simplify the expression.
sin u + tan u + cos u
secu
2
cot x tan x
2
2
4.Use basic identities to simplify the expression. 5.Simplify to a constant or a basic trig function.
sec x − tan x
2
2
cos x + sin x
2
sin x − sin x
3
2
6.Simplify to a constant or a basic trig function. 7. Simplify to a basic trig function.
1 + cot x
1 + tan x
8. Combine the fractions and simplify to a
multiple of a power of a basic trig function.
1
1
+
1 − sin x 1+ sin x
tan x
tan x
+
2
csc x sec 2 x
9. Combine the fractions and simplify to a
multiple of a power of a basic trig function.
sin x
sinx
−
2
cot x cos 2 x
10. Write each expression in factored form as
an algebraic expression of a single trig function.
1 − 2sin x + sin2 x
12. Find all solutions to the equation in the
interval [0,2π )
2 tan x cosx − tan x = 0
14. Find all solutions to the equation in the
interval [0,2π )
2 sin2 x = 1
16. Find all solutions to the equation in the
interval [0,2π )
2 sin2 x + 3sin x = 2
18. Find all solutions to the equation in the
interval [0,2π )
cos x = .75
11. Write each expression in factored form as
an algebraic expression of a single trig function.
cos x − 2 sin2 x + 1
13. Find all solutions to the equation in the
interval [0,2π )
tan x sin2 x = tan x
15. Find all solutions to the equation in the
interval [0,2π )
sin2 x − 2sin x = 0
17. Find all solutions to the equation in the
interval [0,2π )
cos 2 x = .4
19. Prove the identity.
tan x + sec x =
cos x
1 − sin x
20. Prove the identity.
21. Prove the identity.
(1 − sin x )(1 + csc x ) = 1 − sin x + csc x − sin x csc x
sin2 x − cos2 x = 1 − 2 cos2 x
22. Prove the identity.
23. Prove the identity.
sec x + 1
sinx
=
tan x
1− cosx
cot 2 x − cos 2 x = cos2 x cot 2 x
24. Prove the identity.
25. Prove the identity.
1 − cos x
sinx
=
sin x
1+ cosx
cos x
cos x
+
= 2sec x
1 + sin x 1− sin x
26. Use a sum or difference identity to
find an exact value.
27. Use a sum or difference identity to
find an exact value.
sin
7π
12
⎛ π⎞
cos ⎜ − ⎟
⎝ 12 ⎠
28.Write the expression as the sine,
cosine or tangent of an angle.
29.Write the expression as the sine,
cosine or tangent of an angle.
sin 42 cos17 − cos42 sin17
tan 3x − tan 2y
1 + tan 3x tan 2y
30. Prove the identity.
31. Prove the identity
π⎞
⎛
sin ⎜ x − ⎟ = − cosx
⎝
2⎠
π⎞
⎛
tan⎜ x − ⎟ = − cot x
⎝
2⎠
32. Use the appropriate sum or
difference identity to prove.
33. Find all solutions to the equation
cos 2u = 2cos 2 u − 1
[0,2π )
sin2x = 2 sin x
34. Prove the identity.
35. Prove the identity.
cos 6x = 2cos 2 3x − 1
2 csc2x = csc 2 x tan x
36. Prove the identity.
37.Solve algebraically for exact solutions [0,2π )
sin 3x = sin x( 3− 4sin 2 x)
cos 2x + cosx = 0
38. Use half-angle identities to find exact
value without a calculator.
39. Use half-angle identities to find exact
value without a calculator.
sin15 
cos
5π
12
40. Use the 1/2 angle identities to find all solutions
[0,2π )
⎛ x⎞
sin2 x = cos2 ⎜ ⎟
⎝ 2⎠
State whether the given measurements
determine zero, one or two triangles
A = 36 ,a = 2,b = 7
44. Two triangles can be formed using the
given measurements. solve both triangles.
B = 57 ,a = 11,b = 10
41. Solve the triangle.
A = 36 , B = 62, a = 4
43.
State whether the given measurements
determine zero, one or two triangles
C = 30, a = 18,c = 10
45. Solve the triangle.
B = 35 ,a = 43,c = 19
46. Solve the triangle.
47. Find the area of the triangle.
a = 3.2,b = 7.6,c = 6.4
B = 101 ,a = 10cm,c = 22cm
48. Find the area of the triangle.
a = 23,b = 19,c = 12