Find the Exact Value cot(-315 degrees )

Problem

cot(−315)

Solution

1. Find the coterminal angle by adding 360 to the given negative angle to find an equivalent angle between 0 and 360

−315+360=45

2. Identify the trigonometric identity for the cotangent function, which is the ratio of the cosine of the angle to the sine of the angle.

cot(45)=cos(45)/sin(45)

3. Substitute the known values for the sine and cosine of 45 from the unit circle.

cos(45)=√(,2)/2

sin(45)=√(,2)/2

4. Simplify the expression by dividing the two equal values.

√(,2)/2/√(,2)/2=1

Final Answer

cot(−315)=1

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