Question

Which equation shows that the Pythagorean identity is true for 0 = 3π/2?

Select the equation in the form: sin²(3π/2) + cos²(3π/2) = 1.
a) 0² + (-1)² = 1
b) 0² + 1² = 1
c) (-1)² + 1² = 1
d) 1² + 0² = 1

Answer 1

The correct equation that shows the Pythagorean identity is true for 3π/2 is (-1)² + 1² = 1.

Step-by-step explanation:

The Pythagorean identity states that sin²(θ) + cos²(θ) = 1 for any angle θ. In this case, the angle is 3π/2. To determine which equation shows the Pythagorean identity is true for 3π/2, we need to substitute the angle into each option and see which one equals 1.

Substituting 3π/2 into equation a) gives 0² + (-1)² = 1. Substituting into equation b) gives 0² + 1² = 1. Substituting into equation c) gives (-1)² + 1² = 1. Substituting into equation d) gives 1² + 0² = 1.

From these substitutions, we can see that equation c) (-1)² + 1² = 1 is the correct equation, showing that the Pythagorean identity holds for 3π/2.