# Find sin θ if the point on the terminal side is located at (21, 28). Any ideas how to do these?

Find sin θ if the point on the terminal side is located at ( -10, 24).

• (21,28) gives you the legs of the right triangle, but sine is vertical side / hypotenuse. so look at 21,28 and think Pythagorean Theorem. see the common factor of 7? 7(3, 4, guess what? FIVE). hypotenuse is 35, so

sin Θ = 28/35 = 4/5

10 - 24 - H → 2 ( 5 - 12 - 13) .... the 2nd Pythagorean triple you should just KNOW. so hypotenuse is 26, and sin Θ = 24/26 = 12/13.

just plot the terminal point, drop a vertical to the x axis, label sides of the right triangle with their lengths, compute hypotenuse, and get the ratio of sides you need for the trig function. pay attention to negative's in quadrants 2, 3, and 4.

• x=21, y=28

use pithagors theorem to get

hypathɑɲυꜱ

r=sqrt(21^2+28^2)=35

sintheta=opp./hyp.=28/35

theta=sin^-1(28/35)=53deg

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