Trigonometric Equations Part4 | Compound Angles & Multiple Angles

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Trigonometric Equations - Compound Angles, Multiple Angles, Trigonometric Identities
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At 1:38, so that students don't get confused another way is:

Let 'a' be (x+10).
Then solve the equation "sin a = 0.5" in the normal way resulting:
a = 30 or 150
Since a = x+10
Therefore x = 20 and 140

-my-peace
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At 2:47, why do you not take (-1)? What is absolute value? Please explain

-my-peace