Question

use the pythagorean theorem to find the length of the missing side of the right triangle. then find the value of each of the six trigonometric functions of θ.
the length of the missing side of the right triangle is 10
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
find the sine of the angle θ.
\\( \sin \theta = \frac { 3 } { 5 } \\)
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
find the cosine of the angle θ.
\\( \cos \theta = \square \\)
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify sides

Adjacent to $\theta$ is $b = 8$, hypotenuse $c = 10$.

Step3: Calculate cosine

$\cos\theta = \frac{8}{10} = \frac{4}{5}$.

Answer:

$\frac{4}{5}$