Question

Justin wants to evaluate 3cot(-5pi/4). Which of the following identities can he use to help him? Select two answers.

cot(-theta) = cot(theta)
cot(-theta) = -cot(theta)
cot(-theta) = cot(-theta)
cot(theta + pi) = cot(theta)
cot(theta + 2pi) = cot(theta)

Answer 1

I would be the second and fourth one. If this is the test from connexus that is 3 questions:Behavior of Trigonometric Functions Practice the answers are
1. d (4pi)
2. b,d as seen above
3. a,b (f(x)=csc x), (f(x)=1/sin x

Answer 2

`\cot(-\theta)=-\cot(\theta)`

and

`\cot(\theta+\pi)=\cot(\theta)`

Explanation:

Justin wants to evaluate

`3\cot(-(5\pi)/(4))`.

First he can use the fact that, the cotangent function is an odd function and write.

`3\cot((5\pi)/(4))=-3\cot((5\pi)/(4))`.

Also the cotangent function is positive in both the first and third quadrant, so we can use the symmetric property;

`-3\cot(\pi+(\pi)/(4))=-3\cot((\pi)/(4))`.

Hence the correct answers are;

`\cot(-\theta)=-\cot(\theta)`

and

`\cot(\theta+\pi)=\cot(\theta)`