Find the Exact Value sin(-15)

Problem

sin(−15)

Solution

1. Apply the odd function identity for sine, which states that sin(−θ)=−sin(θ)

sin(−15)=−sin(15)

2. Rewrite the angle 15 as a difference of two special angles from the unit circle, such as 45−30

−sin(15)=−sin(45−30)

3. Apply the sine difference formula, sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B) to the expression.

−sin(45−30)=−(sin(45)*cos(30)−cos(45)*sin(30))

4. Substitute the exact values for the sine and cosine of 45 and 30

−(√(,2)/2⋅√(,3)/2−√(,2)/2⋅1/2)

5. Simplify the expression by performing the multiplication and subtraction inside the parentheses.

−(√(,6)/4−√(,2)/4)

6. Distribute the negative sign to find the final exact value.

(√(,2)−√(,6))/4

Final Answer

sin(−15)=(√(,2)−√(,6))/4

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