Question

A point on the terminal side of an acute angle in standard position is (1, 2 √2). Find the cosine value of this angle.

Answer 1

Answer:

$cos\theta=1/3$

Step-by-step explanation:

The point at the terminal side of an acute angle is given by $(1, 2\sqrt{2} )$.

That is,

$x = 1$ and $y= 2\sqrt{2}$ .

Let r be the length of line segment drawn from the origin to the point and is given by the formula:

$r = \sqrt{x^{2} + y^{2}}$

Substituting the values of x and y into r,

$r = \sqrt{1^{2} + (2\sqrt{2} )^{2}}$

$r = \sqrt{1 + 8}$

$r = \sqrt{9}$

Thus, $r=3$

Also, $cos\theta$ is given by:

$cos\theta = x/r$

Substituting values of x and r,

$cos\theta = 1/3$