Cofunction Identities

Show your work for each problem.

1.
What is the cofunction of ?
1. a)
2. b)
3. c)
4. d)
Answer:
The cofunction of sine is cosine. The prefix 'co-' indicates they are cofunctions: .
2.
Two angles are complementary if they sum to:
1. a)
2. b)
3. c)
4. d)
Answer:
Complementary angles sum to (or radians). Supplementary angles sum to .
3.
If , what is ?
Answer: 55
Using : , so .
4.
What is the complement of ?
Answer: 18
The complement of is .
5.
Which identity is correct?
1. a)
2. b)
3. c)
4. d)
Answer:
Tangent and cotangent are cofunction pairs: .
6.
Simplify to the form . What is ?
Answer: 2
Since , we have . Thus , so .
7.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
Since , we know . Therefore .
8.
Verify that
Answer: verified
1. What do and sum to? 90
2. Are tangent and cotangent cofunctions? yes
3. Using the identity, cot(65)
4. Is the identity verified? yes
9.
If , find (in degrees).
Answer: 40
Since , we need . Solving: .
10.
Simplify
Answer: 1
1. Are and complementary? yes
2. Using cofunctions, cos(15)
3. Using cofunctions, sin(15)
4. Substitute: 1
11.
Which of the following equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
The cofunction identity states . The other options are not equivalent.
12.
Solve for : where
Answer: 30
1. Rewrite using cofunction identity sin(90 - theta)
2. Set the arguments equal: . Add to both sides. 3theta = 90
3. Solve for 30
13.
Solve for : where
Answer: 25
Since , we have . So , giving , thus .
14.
Prove that for all
Answer: proven
1. What is equal to using the cofunction identity? sin(theta)
2. Substitute into the fraction: sin(theta)
3. What is ? 1
15.
In radians, the cofunction identity uses which value?
1. a)
2. b)
3. c)
4. d)
Answer:
Since radians, the cofunction identity in radians is .