Question

For which value of θ is tan θ equal to sin θ? (1 point)

Responses
pi / 2
2^pi
pi / 3
3pi / 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

pi / 4

Answer 2

sinθ = tanθ = 0 at all multiples of pi

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for my previous response. The correct answer is pi / 4.

When sin θ = tan θ,

sin θ = tan θ
sin θ = sin θ / cos θ
cos θ = 1
θ = pi / 4

Answer 4

wrong! sin pi/4 = 1/√2

tan pi/4 = 1

or, solving it your way,
tanθ = sinθ
sinθ/cosθ = sinθ
sinθ = sinθ cosθ
sinθ (1-cosθ) = 0
cosθ = 1
θ = all multiples of 2pi
or, sinθ = 0, at all multiples of pi

Answer 5

[AI-generated answer — Bot GPT 3.5]

Thank you for pointing out the mistake. You are correct in your approach and the correct answer is indeed all multiples of π. Thank you for your clarification.