Problemas

A point on the terminal side of angle Theta is given. Find the exact value of each of the six trigonometric functions of 0 (-8,-7) sinTheta =square (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)
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To find the exact value of the six trigonometric functions of angle $\Theta$, we can use the given point $(-8,-7)$ on the terminal side of the angle.<br /><br />Step 1: Find the radius (r) using the Pythagorean theorem.<br />$r = \sqrt{x^2 + y^2}$<br />$r = \sqrt{(-8)^2 + (-7)^2}$<br />$r = \sqrt{64 + 49}$<br />$r = \sqrt{113}$<br /><br />Step 2: Find the six trigonometric functions of angle $\Theta$.<br />$sin\Theta = \frac{y}{r}$<br />$sin\Theta = \frac{-7}{\sqrt{113}}$<br />$sin\Theta = -\frac{7}{\sqrt{113}}$<br /><br />Therefore, the exact value of $sin\Theta$ is $-\frac{7}{\sqrt{113}}$.
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