Chapter 4 Take-home test
Name: _____________________________________
1. Complete the unit circle below. Label degrees, radians, and coordinates.
2. Complete the following below. Give exact, simplified, rationalized solutions.
a. sin (5π/6) = __________
b. cos (-π/2) = __________ c. tan (3π/4) = __________
d. cot (π/3) = ____________
e. sec (0) = __________
f. csc (-2/3) = _____________
g. sin (7π/4) = __________
h. cos () = __________
i. tan (-π/4) = ___________
j. cot (π/6) = __________
k. sec (3π/2) = __________ l. csc (-5π/6) = ____________
m. sin (/4) = __________
n. cos (3/4) = __________ o. tan (5π/3) = ____________
p. cot(3π/4) = ___________
q. sec (π/3) = _________
r. csc (π/4) = _____________
3. Inverse trigonometric functions have a restricted range to insure the function passes the vertical line
test. Give the range for each inverse trig function below.
a. y = sin-1(x) or y = arcsinx
Range: _______________________________
b. y = cos-1(x) or y = arccosx
Range: _______________________________
c. y = tan-1(x) or y = arctanx
Range: _______________________________
4. Answer the following using the unit circle, and not your calculator. Give your answer in radians.
a. sin-1(-1) = ________
b. cos-1 (0) = ________
c. tan-1(0) = ________

3
 = ________
d. sin-1  

2


1
e. cos-1  2  = ________
 
f. tan-1(1) = ________
g. sin-1(0) = ________
 3
 = ________
h. cos-1 

2


 3
 = ________
i. tan-1 

3


1
j. sin-1  2  = ________
 
k. cos-1 (-1) = ________
l. tan-1(  3 ) = ________
 2
m. sin-1  2  = ________



2
n. cos-1   2  = ________



3
 = ________
o. tan-1  

 3 
5. Triangle ABC is a right triangle. Use the Pythagorean theorem to find the missing side, then use SOH,
CAH, TOA, to complete. Give answers as fractions.
B
5
C
12
A
sinA =
cscA =
sinB =
cscB =
cosA =
secA =
cosB =
secB =
tanA =
cotA =
tanB =
cotB =
Give an example of two trigonometric functions that are the same, which trigonometric identity is verified by
the two that you found?
6. If cotθ = ¾, find:
(draw a triangle to help complete the problem)
sinθ =
cscθ =
cosθ =
secθ =
tanθ =
cotθ =
7. Graph y = sinx and y = 2sin2x on the same axes, explain the difference between the two graphs.
8. Graph y = cosx and y = cos(x – π) + 1 on the same axes, explain the difference between the two graphs.
9. Explain how y = secx and y = cscx are graphed from y = cosx and y = sinx. Demonstrate one of
them below.
10. Solve the triangle. Show your work.
The measure of angle C is 90 degrees.
The measure of angle A is 50 degrees.
B
C
10
A
11. Find the altitude of the isosceles triangle. The measures of the base angles
are 50 degrees.
6
12. A 150 foot line is attached to a kite. When the kite has pulled the line taunt, the angle of elevation to the
kite is approximately 55 degrees. Approximate the height of the kite. Draw and label a picture.