Name ______________________________
Sine and Cosine of Complementary Angles
Module 2 Lesson 27
Learning Target: I can use the relationship between the sine and cosine of complementary angles to
solve problems.
Opening Exercise
A. What is 𝑚∠𝐴 + 𝑚∠𝐵? Justify your reasoning.
B. sin 𝐴 = __________
cos 𝐵 = __________
Why is sin 𝐴 = cos 𝐵?
C. sin 𝐵 = __________
cos 𝐴 = __________
Why is sin 𝐵 = cos 𝐴?
Sine and Cosine of Complementary Angles
Sine and Cosine are cofunctions. This means that if 𝑚∠𝐴 + 𝑚∠𝐵 = 90°, in other words two angles
are complementary, then sin 𝐴 = cos 𝐵.
1. sin 30 = cos _______.
2. If cos 72° = sin 𝑥, find the number of degrees in the measure of acute angle x.
3. If sin 6𝐴 = cos 9𝐴, what is 𝑚∠𝐴?
4. For what values of 𝜃 is sin 𝜃 = cos (𝜃 + 10)
5. For what angle measurement must sine and cosine have the same value? Explain how you know.
2
6. If ∠𝐴 is acute and tan 𝐴 = 3, then
1)
2)
3)
4)
There are certain special angles where it is possible to give the exact value of sine and cosine. These
are the angles that measure 0˚, 30˚, 45˚, 60˚, and 90˚; these angle measures are frequently seen.
You should memorize the sine and cosine of these angles with quick recall!
𝜃
0˚
Sine
0
Cosine
1
30˚
1
2
√3
2
45˚
√2
2
√2
2
60˚
√3
2
1
2
7. Use the values on the chart to determine the missing lengths in the triangle.
8. Use the values on the chart to determine the missing lengths in the triangle.
90˚
1
0
Name ______________________________
Sine and Cosine of Complementary Angles
1. Find the value of 𝜃 that makes each statement true.
a. sin 𝜃 = cos(𝜃 + 38)
b. sin 𝜃 = cos(3𝜃 + 20)
𝜃
c. sin ( 3 + 10) = cos 𝜃
2. Determine the value of x.
Module 2 Lesson 27
Problem Set
3. Determine the value of x and y.
4. Given an equilateral triangle with sides of length 9, find the length of the altitude.
Name ______________________________
Sine and Cosine of Complementary Angles
1. Solve: sin 𝐴 = cos 32
2. Solve: cos 𝐵 = sin(𝐵 + 20)
3. △LMN is a 30–60–90 right triangle. Find the unknown lengths x and y.
Module 2 Lesson 27
Exit Ticket