Algebra 2
Chapter 13 Test Review
1
Name: ______________
Date_______Per
The diagram below shows right triangle UPC.
Evaluate the following:
sin U =
csc U =
cos U =
sec U =
tan U =
cot U =
2 A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle
ABC measuring 45 degrees and radius
a) What is the length of arc AC, in feet?
feet. (Give exact answer.)
b) What is the area of the sector?
3.
Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular
walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures
radians, what is the length, in yards, of the border?
4 As shown in the accompanying diagram, a dial in the shape of a semicircle has a radius of 4 centimeters.
Find the measure of θ, in radians, when the pointer rotates to form an arc whose length is 1.38
centimeters.
6) Express 330º in radian measure.
7) Express 330º in radian measure.
8) Express
9) Express
radians in degree measure.
radians in degree measure.
10 List a positive angle between 0º and 360º that is coterminal to 985º.
11 List a negative angle between 0 and -2π radians that is coterminal to
7𝜋
2
.
12 Circle all angles that are coterminal to 1125⁰.
a.
g.
60⁰
9𝜋
4
b. -45⁰
h.
5𝜋
4
c. 45⁰
i.
−𝜋
4
d. 445⁰
𝜋
j. 4
e. 820⁰
k.
−7𝜋
4
For problems 13-16, find the length of each missing side in simplest radical form.
f. 765⁰
l.
−15𝜋
4
For problems 17-22, evaluate using the Unit Circle. Label the diagram, label the reference angle, and
label the sides before evaluating. Give exact answers. No decimals. Rationalize denominators.
5𝜋
17) sin 180⁰
18) cos 6
19) cot(-330⁰)
20) csc 60⁰
21) sec
3𝜋
22) tan 135⁰
2
For #23-28, sketch the graph of each circle. Identify the radius of the circle.
23. (𝑥 + 1)2 + (𝑦 − 1)2 = 16
24. 2𝑥 2 + 2𝑦 2 = 10
radius: ______
radius: ______ center : (___, ____)
center (____, _____)
Write the equation of each circle.
25.
27. Passes through (-6, 8) with center at (0, 0)
26.
28. Passes through (-8, -5) with center at (0, 0)