Find the Other Trig Values in Quadrant II cot(x)=-2

Problem

cot(x)=−2, Quadrant II

Solution

1. Identify the given information and the constraints of the quadrant. In Quadrant II, x is negative and y is positive. Since cot(x)=x/y=−2 we can let x=−2 and y=1

2. Calculate the radius r using the Pythagorean identity r=√(,x2+y2)

r=√(,(−2)2+(1)2)

r=√(,4+1)

r=√(,5)

3. Determine the value of tan(x) by taking the reciprocal of cot(x)

tan(x)=1/cot(x)

tan(x)=−1/2

4. Determine the value of sin(x) using the ratio y/r and rationalize the denominator.

sin(x)=1/√(,5)

sin(x)=√(,5)/5

5. Determine the value of csc(x) by taking the reciprocal of sin(x)

csc(x)=√(,5)

6. Determine the value of cos(x) using the ratio x/r and rationalize the denominator.

cos(x)=(−2)/√(,5)

cos(x)=−(2√(,5))/5

7. Determine the value of sec(x) by taking the reciprocal of cos(x)

sec(x)=−√(,5)/2

Final Answer

sin(x)=√(,5)/5,cos(x)=−(2√(,5))/5,tan(x)=−1/2,sec(x)=−√(,5)/2,csc(x)=√(,5)

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