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Sum and Difference Formulas for Sine
sin(a + b) = sin a cos b + cos a sin b
sin(a - b) = sin a cos b - cos a sin b
Sin Function
Helpful hints:
Sine's Sum and Difference Formulas will always include sin a cos b
If adding a + b, the sign between sin a cos b will be +
If subtracting a - b, the sign between sin a cos b will be -
Find the Sum of Two Given Angles and Their Quadrants
Example 1
Unlike the cosine examples, which ask us to find the exact value of an angle (without using a calculator), the example below wants us to find the exact value of the sum of two angles.
Given are two angles, their values, and their quadrant location.
Let's look at the problem
Part I
Before applying this information to the sine's additions formula, we need to ensure we have all the values to complete the formula. Use the Pythagorean Identity to find cos a and cos b.
Part II
Once we have the values for these trig angles, we plug these values into the formula and complete the problem during the math.
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