Find the exact values of sinalpha ,cosalpha ,tanalpha ,cscalpha ,secalpha and cotalpha where a is an angle in standard position whose terminal side contains the point (-8,-8) Find sinalpha Select the correct choice below and, if necessary.fill in the answer box to; complete your choice. A. sinalpha =square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression ) B. sinalpha is undefined.

Question

Problemas

$Find the exact values of sinalpha ,cosalpha ,tanalpha ,cscalpha ,secalpha and cotalpha where a is an angle in standard position whose terminal side contains the point (-8,-8) Find sinalpha Select the correct choice below and, if necessary.fill in the answer box to; complete your choice. A. sinalpha =square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression ) B. sinalpha is undefined.$

Find the exact values of sinalpha ,cosalpha ,tanalpha ,cscalpha ,secalpha and cotalpha where a is an angle in standard position whose terminal side contains the point (-8,-8) Find sinalpha Select the correct choice below and, if necessary.fill in the answer box to; complete your choice. A. sinalpha =square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression ) B. sinalpha is undefined.

Answer 1

To find the exact values of the trigonometric functions, we first need to determine the angle $\alpha$ whose terminal side contains the point $(-8,-8)$. We can do this by finding the reference angle and then using the appropriate quadrant. Step 1: Find the reference angle. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. Since the point $(-8,-8)$ is in the third quadrant, we can use the Pythagorean theorem to find the reference angle. Let $x = -8$ and $y = -8$. Then, $r = \sqrt{x^2 + y^2} = \sqrt{(-8)^2 + (-8)^2} = \sqrt{64 + 64} = \sqrt{128} = 8\sqrt{2}$. The reference angle is $\theta = \arctan\left(\frac{y}{x}\right) = \arctan\left(\frac{-8}{-8}\right) = \arctan(1) = \frac{\pi}{4}$. Step 2: Determine the angle $\alpha$. Since the point $(-8,-8)$ is in the third quadrant, the angle $\alpha$ is $\pi + \theta = \pi + \frac{\pi}{4} = \frac{5\pi}{4}$. Step 3: Find the trigonometric functions. Using the angle $\alpha = \frac{5\pi}{4}$, we can find the trigonometric functions as follows: $\sin\alpha = \sin\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$ $\cos\alpha = \cos\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$ $\tan\alpha = \tan\left(\frac{5\pi}{4}\right) = 1$ $\csc\alpha = \csc\left(\frac{5\pi}{4}\right) = -\sqrt{2}$ $\sec\alpha = \sec\left(\frac{5\pi}{4}\right) = -\sqrt{2}$ $\cot\alpha = \cot\left(\frac{5\pi}{4}\right) = 1$ Therefore, the correct choice is A. $\sin\alpha = -\frac{\sqrt{2}}{2}$.

Problemas

Solución

Responder