Question

which portion of the unit circle satisfies the trigonometric inequality $cos^{2}\theta+sin^{2}\theta>1$? assume that $\theta$ is the angle made by the positive x - axis and a ray from the origin. all of the unit circle the top half of the unit circle the right half of the unit circle none of the unit circle

Explanation:

Step1: Recall the Pythagorean identity

By the Pythagorean identity in trigonometry, for any angle $\theta$, $\cos^{2}\theta+\sin^{2}\theta = 1$.

Step2: Analyze the inequality

The given inequality is $\cos^{2}\theta+\sin^{2}\theta>1$. Since $\cos^{2}\theta+\sin^{2}\theta$ is always equal to 1 for all real - valued angles $\theta$, there is no value of $\theta$ (no part of the unit circle) for which $\cos^{2}\theta+\sin^{2}\theta>1$. So the answer is none of the unit circle.

Answer:

none of the unit - circle