angles and fractions

Question

if the terminal side of an angle theda, in standard position, passes through the point (8, -6), what is the value of sin theda

Answer 1

Hello Tialah,

(i) Plot the coordinate (8,-6), which would land in the fourth quadrant

(ii)

a) Draw a line from the origin to the coordinate.

b) Then draw a line from the coordinate perpendicularly back to the nearest x-axis

c) You should now have a right triangle formed

iii) In this right triangle, label the angle nearest the origin with Θ.

iv) Label the horizontal side of the triangle with 8 and the vertical side with -6.

v) By Pythagorean, find the value of the hypotenuse, which will be 10.

vi) From SOHCAHTOA, sin(Θ) = -6 / 10 = -3 / 5.

I hope the above helps, and thank you for the question.

Michael Ehlers