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

Want more problems? Check here!