Question

find the six trigonometric function values of the specified angle. sin θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find the hypotenuse

By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 5$ and $b=7$. So $c=\sqrt{5^{2}+7^{2}}=\sqrt{25 + 49}=\sqrt{74}$.

Step2: Calculate $\sin\theta$

The definition of $\sin\theta$ in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. The opposite side to angle $\theta$ is 7 and the hypotenuse is $\sqrt{74}$. So $\sin\theta=\frac{7}{\sqrt{74}}=\frac{7\sqrt{74}}{74}$.

Answer:

$\frac{7\sqrt{74}}{74}$