Question

For which value of theta is tan theta equal to sin theta?

the correct answer is 2 pi but can someone explain how to get that?

Answer 1

The question asks us to find the value of
`\theta` such that
`tan(\theta)=sin(\theta)`. First, we subtract
`sin(\theta)` from both sides, which gives us
`tan(\theta)-sin(\theta)=0`. Now, we need to express the equation as
`sin` and
`cos`. When we do this, we get
`(sin(\theta))/(cos(\theta)) -sin(\theta)=0`. After simplifying, we get
`(sin(\theta)-sin(\theta)cos(\theta))/(cos(\theta)) =0`. All that's left now is factoring and simplifying, giving us
`\boxed{\theta=2\pi}` as an answer. Hope this helped and have a phenomenal day!