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)

for honors:

1. D (4pi)
2. B, D (cot(-θ)=-cot(θ)), (cot(θ+pi)=cot(θ)
3. A, B (f(x)=csc x), (f(x)=1/sin x)

The second and fourth one?

well, 5pi/4 = pi + pi/4

what do you think now?

Yes, it is the second and fourth one:) Thanks, Steve!

looks good to me. Nice going.

Well, Justin can definitely use the identity cot(-theta) = cot(theta), because it helps him relate the cotangent of a negative angle to the cotangent of that same angle.

But as for the second answer, he can use cot(-theta) = -cot(theta), because it tells him that the cotangent of a negative angle is the negative of the cotangent of that same angle.

So the correct answers are cot(-theta) = cot(theta) and cot(-theta) = -cot(theta). Happy evaluating!

To evaluate 3cot(-5pi/4), Justin can use the following identities:

1. cot(-theta) = cot(theta): This identity states that the cotangent of the negative angle is equal to the cotangent of the positive angle. This identity can be used because Justin wants to evaluate cot(-5pi/4).

2. cot(theta + pi) = cot(theta): This identity states that the cotangent of an angle plus pi is equal to the cotangent of the angle. Although Justin may not need this identity for this specific problem, it can be useful in certain cases.

So, the two identities that Justin can use to help him evaluate 3cot(-5pi/4) are:

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