SOLUTION: how would i show that sin (-θ) = -sin θ

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Question 482144: how would i show that sin (-θ) = -sin θ
Found 2 solutions by lwsshak3, jim_thompson5910:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
how would i show that sin (-θ) = -sin θ
using x in place of theta
..
Explaining it graphically:
By convention, positive angle are rotated counter-clockwise, and negative angles, clockwise.
The sin of an angle in quadrants I and II are always positive and in quadrants III and IV always negative.
For example, if the angle is positive and less than 180º sin x will be positive in quadrants I and II, but if the angle is negative, you will reverse direction and end up in quadrants II or IV where sin x will be negative. No matter what the angle, sin (-x)=-sin x. Try it with any angle. Hope this helps.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin(-θ) = sin(0-θ)


sin(-θ) = sin(0)cos(θ)-cos(0)sin(θ)


sin(-θ) = 0*cos(θ)-1*sin(θ)


sin(-θ) = 0-sin(θ)


sin(-θ) = -sin(θ)