Question

Use the pythagorean theorem to prove that this point lies on the unit circle. Find csc(0) where 0=-120.

Answer 1

By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.

How to prove this point lies on the unit circle?

In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 120

Reference angle = 60°.

For the coordinates, we have:

sin(-120) = -sin(60) = -1/2.

cos(-120) = -cos(60) = -√3/2.

By applying Pythagorean theorem, we have:

z² = x² + y²

z = √((-1/2)² + (-√3/2)²)

z = √(1/4 + 3/4)

z = √1

z = 1.

Read more on unit circle here: brainly.com/question/9797740

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