Question

what is the value of sec θ given the diagram below? (-3, 6) θ -√5 -√5/2 √5/2

Explanation:

Step1: Find the value of $r$

Use the formula $r=\sqrt{x^{2}+y^{2}}$, where $x = - 3$ and $y = 6$. So $r=\sqrt{(-3)^{2}+6^{2}}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}$.

Step2: Recall the definition of cosine

The definition of $\cos\theta=\frac{x}{r}$. Here, $x=-3$ and $r = 3\sqrt{5}$, so $\cos\theta=\frac{-3}{3\sqrt{5}}=-\frac{1}{\sqrt{5}}$.

Step3: Recall the definition of secant

Since $\sec\theta=\frac{1}{\cos\theta}$, substituting the value of $\cos\theta$ we get $\sec\theta=-\sqrt{5}$.

Answer:

$-\sqrt{5}$