Find the Exact Value cot(480)

Problem

the cotangent of 480 raised to the composed with power

Solution

1. Find the coterminal angle by subtracting 360 raised to the composed with power from 480 raised to the composed with power to bring the angle within the standard range of 0 raised to the composed with power to 360 raised to the composed with power

480 raised to the composed with power minus 360 raised to the composed with power equals 120 raised to the composed with power

2. Identify the quadrant for 120 raised to the composed with power Since 90 raised to the composed with power is less than 120 raised to the composed with power is less than 180 raised to the composed with power the angle lies in Quadrant II.

3. Determine the reference angle for 120 raised to the composed with power in Quadrant II by subtracting the angle from 180 raised to the composed with power

180 raised to the composed with power minus 120 raised to the composed with power equals 60 raised to the composed with power

4. Apply the trigonometric sign for the cotangent function in Quadrant II. In Quadrant II, cotangent theta is negative.

the cotangent of 120 raised to the composed with power equals negative the cotangent of 60 raised to the composed with power

5. Evaluate the exact value using the known value for the cotangent of 60 raised to the composed with power equals the fraction with numerator the square root of 3 and denominator 3

negative the cotangent of 60 raised to the composed with power equals negative the fraction with numerator the square root of 3 and denominator 3

Final Answer

the cotangent of 480 raised to the composed with power equals negative the fraction with numerator the square root of 3 and denominator 3

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