Question

score: 9/13 answered: 12/13 question 13 the point (5, 7) lies on the terminal side of the angle ∠a in the standard (x, y) coordinate plane shown below. what is the value of cos(a)? question help: video check answer

Explanation:

Step1: Recall cosine formula in coordinate - plane

For an angle $\angle A$ in standard position with a point $(x,y)$ on its terminal side, $\cos(A)=\frac{x}{r}$, where $r = \sqrt{x^{2}+y^{2}}$.

Step2: Calculate $r$

Given $x = 5$ and $y = 7$, then $r=\sqrt{5^{2}+7^{2}}=\sqrt{25 + 49}=\sqrt{74}$.

Step3: Calculate $\cos(A)$

Since $x = 5$ and $r=\sqrt{74}$, $\cos(A)=\frac{5}{\sqrt{74}}$.

Answer:

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