Competency Review 4: Trigonometry
Group Name: _____________________________________________________________________
Table No: ________


19. Graph f ( x)  cos  x    1 below. Be sure to label all key points on the x and y axes.
2

Amplitude:______
Period:_________
20. Give the domain and range of y = cos x.
21. Give the domain and range of y = tan x.
Hint: Recall that inverse functions are
reflections of each other across the
diagonal y = x since the domain (x's) of
one becomes the range (y's) of the
other. Only 1-1 functions have inverses,
so we select a section of the original
function that passes both the vertical
and horizontal line test. Go to the
review slideshow if you need more help
with inverses.
 
22. Since the point is on  ,1 y = sin x, what related point is on y = sin-1 x?
2 
23. Since the point  , 1 is on y = cos x, what related point is on y = cos x?
-1
24. Graph each inverse trig function. Be sure to label key coordinates on each axis.
-1
A. y = sin x
-1
B. y = cos-1 x
C. y = tan x
25. Give the equations of two asymptotes on the graph of y = tan x and the equations of two asymptotes on the
-1
graph of y = tan x.
26. Solve each equation over [0, 2 ):
x 1
A. cos 
B. 2sin(3x) –
2 2
3 =0
C. 3tan 2 x  1
27. Find ALL solutions of x given tan x < 0 and 4cos2x – 1 = 0.
28. Simplify each expression over the proper domain and range of the function.

1
2
A. arc cos  
B. sin 1
C. tan 1  1

2
 2 
D. sec1 2
29. Write a PYTHAGOREAN IDENTITY involving each ratio shown below.
A. sin
B. csc
C. tan
30. Complete each COFUNCTION IDENTITY below.


A. cos   x  
2



B. sec   x  
2



C. cot   x 
2

31. (Use results from #30.) If sin
7
a
1
  , find cos  .
18
b
9
32. Use a NEGATIVE ANGLE IDENTITY to answer each true/false question below.
T
F A. For all values of x, cos x = cos (– x). Hint: Think of cos
T
F B. For all values of x, sin x = sin (– x).
T
F C. For all values of x, tan x = tan (– x).
2
2
and cos (–
), for example.
3
3
33. Complete the DOUBLE ANGLE IDENTITY for each.
A. sin 2x =
B. cos 2x =
C. tan 2x =
True or False.
T
F 34. The graph of y = – tan x is a reflection of y = tan x across the y-axis.
T
F 35. In quadrant II cosine is positive.
T
F 36. In quadrant IV tangent is positive.
T
F 37. If the lengths of the legs of a right triangle are 5 and 12, then the hypotenuse is 13.
T
F 38. The point on the unit circle that corresponds to
T
F 39.
T

5
and 
are coterminal angles.
3
3


F 40. and – have the same cosine value.
4
4
F 41. The amplitude of y = 2 sin 3x is three.
T
F 42. The period of y = 3 sin 4x is 2  .
T
F 43. (0, 1) is a point on the graph of y = cos x.
T
F 44. y = cot x has a vertical asymptote at x = -1.
T
F 45. For all values of x, 1 + cot x = csc x.
T
2
2
7
radians is
6

3 1
,  
 
2
 2