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Name _____________________________________________
Review for Trigonometry Unit 2 Test
Topics in Trigonometry
Test Topics:
•
•
•
•
•
Reciprocal Trig. Functions
Co-functions
Radian Measure
Arc Length
Evaluating Trigonometric Functions using the Reciprocal Functions & Radian Measure
Review Questions
1. In a circle of radius of 8 inches, find the length of the intercepted arc by a central angle of
1.5 radians.
2. In a circle, a central angle measuring 30° intercepts an arc of 10 cm. Find the length of the
radius.
3. A circle has a radius of 6 cm. What is the number of radians in the central angle that
creates an arc of length 12 cm?
4. Find the exact value of cos
ଷగ
6. Find the exact value of tan
ଷగ
ସ
ଶ
଻గ
.
5. Find the exact value of sin
.
7. Find the exact value of cos(− ߨ).
଺
.
గ
8. Find the exact value of sec 30° ⋅ tan ߨ.
10. Find the exact value of ቀcos
ଷగ ଶ
9. Find the exact value of csc + cot
ଶ
గ
ቁ + csc ଺ .
ସ
11. Find the exact value of cot 300°.
ଶ
12. If sin ‫ = ݔ‬− ଷ and cos ‫ > ݔ‬0, find:
a. the quadrant in which ∠‫ ݔ‬lies
b. tan ‫ݔ‬
d. sec ‫ݔ‬
f. cot ‫ݔ‬
e. csc ‫ݔ‬
13. If tan ‫ = ݔ‬−2 and sin ‫ > ݔ‬0, find:
a. the quadrant in which ∠‫ ݔ‬lies
d. sec ‫ݔ‬
e. csc ‫ݔ‬
14. Name the quadrant in which ∠‫ ܣ‬lies given:
a. cot ‫ < ܣ‬0 and cos ‫ > ܣ‬0
c. sec ‫ > ܣ‬0 and tan ‫ < ܣ‬0
b. sin ‫ݔ‬
f. cot ‫ݔ‬
b. csc ‫ < ܣ‬0 and sec ‫ < ܣ‬0
d. cot ‫ > ܣ‬0 and csc ‫ > ܣ‬0
c. cos ‫ݔ‬
c. cos ‫ݔ‬
଻గ
ସ
.
15. If point P (−3, 4) lies on the terminal side of an angle, ߠ, in standard position. Evaluate all six
trigonometric functions of angle ߠ, in simplest radical form if necessary.
16. If point P (1, −2) lies on the terminal side of an angle, ߠ, in standard position. Evaluate all six
trigonometric functions of angle ߠ, in simplest radical form if necessary.
17. Identify the three pairs of co-functions.
(1)
(2)
(3)
18. If a pair of co-functions have equal ratios, then the angles of the functions have what
relationship?
19. Solve for x: sin(‫ ݔ‬+ 10) = cos(3‫ ݔ‬+ 8)
20. Solve for a: sec(2ܽ − 9) = csc ܽ
21. Solve for y: tan(2‫ = )ݕ‬cot(3‫ ݕ‬− 10)
22. Write tan 310° as a function of a positive acute angle that measures less than 45°.
23. Write sec 260° as a function of a positive acute angle that measures less than 45°.
24. Express each radian measure in degrees:
గ
ଷగ
b. ߨ
c. ଶ
d. 2ߨ
a. ଶ
h.
గ
଺
i.
ଷగ
j.
ସ
ହగ
଺
k.
ଽగ
ଶ
e. 4ߨ
l. −
ଷగ
ଶ
25. Express each degree measure in radian measure:
a. −90°
b. 120°
c. 210°
e. 450°
Remember:
• Special Right Triangles
• Unit Circle
• Degrees to Radians
• Radians to Degrees
•
•
•
•
f.−150°
g. 135°
ଵ
ଵ
Reciprocal functions: sec ‫ = ݔ‬ୡ୭ୱ ௫
csc ‫ = ݔ‬ୱ୧୬ ௫
3 pairs of co-functions
Angle relationship between co-functions
h. 330°
ଵ
cot ‫୲ = ݔ‬ୟ୬ ௫
గ
g.
ଷ
m. −
d. 240°
௦
Formula for arc length ߠ = ௥
f.
ହగ
ଵଶ
n.
గ
ସ
ଶగ
ହ