Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 10, 2023

Evaluate the expression $\sin^2 150^\circ + \cos^2 150^\circ$ and simplify the result.

STEP 1

Assumptions1. The expression is $\sin ^{}150^{\circ}+\cos ^{}150^{\circ}$ . . We are working in degrees, not radians.
3. We are using the Pythagorean identity for sine and cosine, which states that for any angle $\theta$ , $\sin^ \theta + \cos^ \theta =1$ .

STEP 2

The expression is a direct application of the Pythagorean identity for sine and cosine. We can substitute the identity into the expression.
$\sin ^{2}150^{\circ}+\cos ^{2}150^{\circ} =1$

STEP 3

The expression simplifies to1, which is the final answer.
$\sin ^{2}150^{\circ}+\cos ^{2}150^{\circ} =1$ The expression $\sin ^{2}150^{\circ}+\cos ^{2}150^{\circ}$ evaluates to1.

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