Find the Other Trig Values in Quadrant IV cot(theta)=-1/5

Problem

cot(θ)=−1/5,θ∈Quadrant IV

Solution

1. Identify the given information and the quadrant. In Quadrant IV, x is positive and y is negative.

2. Relate the cotangent function to the coordinates x and y using the definition cot(θ)=x/y

3. Assign values to x and y based on the quadrant. Since cot(θ)=1/(−5) let x=1 and y=−5

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

r=√(,1+(−5)2)

r=√(,1+25)

r=√(,26)

5. Determine the value of tan(θ) by taking the reciprocal of cot(θ)

tan(θ)=1/cot(θ)=−5

6. Determine the value of sin(θ) using the ratio y/r

sin(θ)=(−5)/√(,26)=−(5√(,26))/26

7. Determine the value of cos(θ) using the ratio x/r

cos(θ)=1/√(,26)=√(,26)/26

8. Determine the value of csc(θ) using the ratio r/y

csc(θ)=√(,26)/(−5)=−√(,26)/5

9. Determine the value of sec(θ) using the ratio r/x

sec(θ)=√(,26)/1=√(,26)

Final Answer

sin(θ)=−(5√(,26))/26,cos(θ)=√(,26)/26,tan(θ)=−5,csc(θ)=−√(,26)/5,sec(θ)=√(,26)

Want more problems? Check here!