Question

Find the cosθ if an angle is in standard position and the point with coordinates (7,24) lies on the terminal side of an angle.

Answer 1

0.28

Explanation:

Angles in standard position are angles with the initial side on the positive x-axis.

Since (7,24) lies on the terminal side of an angle, hence the line passing through the origin and point (7, 24) forms an angle with the x axis.

The slope of the line passing through the origin (0, 0) and the point (7, 24) is given by:

`slope(m)=(y_2-y_1)/(x_2-x_1)\\\\m=(24-0)/(7-0)\\\\m=(24)/(7 )`

The angle θ between a straight line and the x axis is:

tanθ = m

where m is the slope of the line.

Let θ be the angle between the line with a slope of 24/7 and the x axis, therefore:

tanθ = 24 / 7

θ = tan⁻¹(24/7)

θ = 73.74°

cosθ = cos(73.74°) = 0.28