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.

1/3

1

2√2/3

2√2

Answer 1

`cos\theta=1/3`

Explanation:

The point at the terminal side of an acute angle is given by
`(1, 2√(2) )`.

That is,

`x = 1` and
`y= 2√(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√(2) )^(2)}`

`r = √(1 + 8)`

`r = √(9)`

Thus,
`r=3`

Also,
`cos\theta` is given by:

`cos\theta = x/r\\`

Substituting values of x and r,

`cos\theta = 1/3\\`