# How do I solve a sum and difference trig equation for the smallest positive solutions?

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#sin(6x)cos(8x)-cos(6x)sin(8x) = -0.7# .

This is what I have so far:

simplify #sin(x)# .

#sin(6x-8x) = -0.7#

#sin(-2x) = -0.7#

#-sin(2x) = -0.7#

solve for #x# .

#2x = theta#

#x = 1/2 theta#

solve for #theta# .

#sin(theta) = -0.7#

#sin(theta) = ???#

This is what I have so far:

simplify

solve for

solve for

##### 1 Answer

Jun 27, 2018

#### Explanation:

sin 6x.cos 8x - cos6x.sin 8x = -0.7

sin (6x - 8x) = sin (-2x) = - sin 2x = - 0.7

sin 2x = 0.7

Calculator and unit circle give 2 solutions for 2x:

a.

If k = 0 -->

If k = 1 -->

b.

The 2 smallest positive answers are: