Download Unit 6a Review - Saugerties Central School

Unit 6a Review
1. In the diagram of right triangle JTM,
What is the value of
1)
,
, and
.
?
2) 2
3)
4)
2. If
1)
2)
3)
4)
and
, in which quadrant does the terminal side of
lie?
I
II
III
IV
3. If the terminal side of angle
passes through point
, what is the value of
?
1)
2)
3)
4)
4. (9 points) Fill in the following chart with exact values for each trigonometric function:

30°
sin 
cos
tan 
1
45°
60°
 8 15 
,  , answer the following questions:
 17 17 
5. If the terminal side of ø intersects the unit circle at  
a. sinø=
b. cosø=
c. tanø=
d. In what quadrant does ø lie?
6. Solve for . Round to the nearest degree. tan =6 .
7. Find the exact value of cos 210 . Show your work.
8. Use the unit circle to find the exact value of sin(270°). Show your work.
9. Simplify the following expression: tan(30°)+ cos(30) - sin(30).
10. Express sin(312°) as a function of a positive acute angle.
11. Express cos(312°) as a function of a positive acute angle.
2
12. If  is an acute angle and cot  
13. A central angle of
1
, find the values of the other five trigonometric functions.
3

radians subtends an arc of 20 centimeters. How many centimeters are in the radius of the circle to
4
the nearest tenth?
14. Draw an angle of -550° in standard position.
15. Find the exact value of the point on the unit circle intersected by an angle of 135°.
16. Find the exact value of cot(60°). Show your work.
17. Find the smallest positive angle coterminal with 910°.
3
18. Convert 170° to radians. Leave your answer in terms of π.
19.  is an angle in standard position that passes through the point (-3,-6).
a. (2 points) Find the value of cot  .
b. (2 points) Find the value of cos  .
20. Find the length of the arc subtended by an angle of 4 radians if the radius of the circle is 4.5 feet.
21. If
1)
2)
3)
4)
and
, then
terminates in Quadrant
I
II
III
IV
22. Find the value of cscA and tanA.
A
4
C
CC
4
B
7
1
23. If the terminal side of  intersects the unit circle at  , 

2
24. Which expression is equivalent to
1) cos 60
2) cos30
3)  cos60
4)  cos30
3
 , find  in both degrees and radians.
2 
?
25. Simplify the following expression: tan 45  cos 45 tan 60
26. Find the reference angle for 250°. Sketch the original angle in standard position. Label the reference angle in your
sketch.
27. Find the exact value of the point on the unit circle intersected by an angle of 240°.
5
28. Find the exact value of sec(90°) using the unit circle. Show your work.
29. Convert
4
radians to degrees.
9


30. Find the exact value of tan 120 . Show your work.
6