Question

question 7 of 10
which equation shows that the pythagorean identity is true for θ = 2π? select the equation that is in the form sin²(2π) + cos²(2π) = 1.

a. 0² + 1² = 1
b. (-1)² + 0² = 1
c. 0² + (-1)² = 1
d. 1² + 0² = 1

Explanation:

Step1: Find sin(2π) and cos(2π)

We know from the unit circle that $\sin(2\pi) = 0$ and $\cos(2\pi)=1$.

Step2: Substitute into the Pythagorean identity

The Pythagorean identity is $\sin^{2}(\theta)+\cos^{2}(\theta) = 1$. For $\theta = 2\pi$, we substitute $\sin(2\pi)=0$ and $\cos(2\pi) = 1$ into the identity. So we get $\sin^{2}(2\pi)+\cos^{2}(2\pi)=0^{2}+1^{2}$.

Step3: Check the equation

Now we check the equation $0^{2}+1^{2}=1$. Calculating the left - hand side: $0^{2}=0$ and $1^{2}=1$, so $0 + 1=1$, which is a true statement.

Answer:

A. $0^{2}+1^{2}=1$