Reciprocal Identities

Show your work for each problem.

1.
What is the reciprocal identity for cosecant?
1. a)
2. b)
3. c)
4. d)
Answer:
Cosecant is defined as the reciprocal of sine:
2.
If , what is ?
Answer: 2
3.
Which function is the reciprocal of cosine?
1. a)Secant
2. b)Cotangent
3. c)Tangent
4. d)Cosecant
Answer: Secant
Secant is the reciprocal of cosine: . Note: cosine pairs with secant (not cosecant).
4.
If , what is ? (Give as a decimal)
Answer: 0.25
5.
Find
Answer: 2
1. What is ? 1/2
2. Apply the reciprocal identity: 2
6.
Which expression equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Simplify:
Answer: 1
1. Replace with its reciprocal form 1/sin(theta)
2. What is ? 1
8.
If , what is ? (Use decimal, round to 2 places)
Answer: 1.15
9.
At which angle is undefined?
1. a)
2. b)
3. c)
4. d)
Answer:
is undefined when . Since , is undefined.
10.
Find
Answer: 1
1. What is ? 1
2. Apply: 1
11.
If , what is ? (Give as fraction like 12/5)
Answer: 12/5
12.
Simplify:
Answer: cot(theta)
1. Rewrite using sine 1/sin(theta)
2. Rewrite using cosine 1/cos(theta)
3. Simplify cos(theta)/sin(theta)
4. What is called? cot(theta)
13.
Which expression simplifies to ?
1. a)
2. b)
3. c)
4. d)
Answer:
because secant is the reciprocal of cosine.
14.
Find (exact value)
Answer: sqrt(2)
1. What is ? sqrt(2)/2
2. Apply 2/sqrt(2)
3. Rationalize: sqrt(2)
15.
If , what is ? (Give as decimal)
Answer: 0.2
If , then
16.
Simplify:
Answer: 2
1. What is ? 1
2. What Pythagorean identity relates and ? sec^2 = 1 + tan^2
3. So 1
4. Final answer: 2