Draw a graph of f(θ)= sin(θ+2)

Question

I'm not able to understand the following graph. Because of θ + 2 the graph is starting at 2 units left of 0. But how do I get those points? For eg. if I put θ =-2, it'll be sin(0)=0. But how do I get point of 1 and -1 on Y-axis? I thought only sin(π/2) =1 and sin(3π/2) =-1. But I'm not sure how do I put π/2 in this equation? I'm also aware of the concept of phase shift.

Answer 1

Set $\theta + 2 = \frac{\pi}{2} \implies \theta = \frac{\pi}{2} - 2$. You can do the same thing for $\frac{3\pi}{2}$.