find all solutions to the equation. sin θ - 1 = 0 write your answer in radians in terms of π, and use the…

find all solutions to the equation. sin θ - 1 = 0 write your answer in radians in terms of π, and use the \or\ button as necessary. example: θ = π/5 + 2kπ, k ∈ z or θ = π/7 + kπ, k ∈ z

find all solutions to the equation. sin θ - 1 = 0 write your answer in radians in terms of π, and use the \or\ button as necessary. example: θ = π/5 + 2kπ, k ∈ z or θ = π/7 + kπ, k ∈ z

Answer

Explanation:

Step1: Isolate the sine - function

Add 1 to both sides of the equation $\sin\theta - 1=0$. $\sin\theta=1$

Step2: Recall the unit - circle values

We know that on the unit - circle, $\sin\theta = y/r$. When $\sin\theta = 1$, and $r = 1$, $y = 1$. The angle $\theta$ for which $\sin\theta=1$ in the interval $[0,2\pi)$ is $\theta=\frac{\pi}{2}$. Since the sine function has a period of $2\pi$, the general solution is $\theta=\frac{\pi}{2}+2k\pi,k\in\mathbb{Z}$.

Answer:

$\theta=\frac{\pi}{2}+2k\pi,k\in\mathbb{Z}$