Simplify sin(-315)

Problem

sin(−315)

Solution

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

sin(−315)=−sin(315)

2. Find the coterminal angle or reference angle for 315 Since 315 is in the fourth quadrant, the reference angle is 360−315=45

315=360−45

3. Determine the sign of the sine function in the fourth quadrant. Since sine is negative in the fourth quadrant, sin(315)=−sin(45)

−sin(315)=−(−sin(45))

4. Simplify the signs to show that the expression is equivalent to the sine of the reference angle.

−(−sin(45))=sin(45)

5. Substitute the known value for sin(45) which is √(,2)/2

sin(45)=√(,2)/2

Final Answer

sin(−315)=√(,2)/2

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