Question

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

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  $\frac{sin(\theta)}{cos(\theta)} -sin(\theta)=0$. After simplifying, we get $\frac{sin(\theta)-sin(\theta)cos(\theta)}{cos(\theta)} =0$. 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!