Question

find the six trigonometric function values of the specified angle. tan θ = 7/5 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) sec 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: Define secant

The secant of an angle in a right - triangle is $\sec\theta=\frac{c}{a}$, where $c$ is the hypotenuse and $a$ is the adjacent side to the angle $\theta$.
Since $c = \sqrt{74}$ and $a = 5$, then $\sec\theta=\frac{\sqrt{74}}{5}$.

Answer:

$\frac{\sqrt{74}}{5}$