Find the Other Trig Values in Quadrant IV cos(x)=4/5

Problem

cos(x)=4/5,x∈Quadrant IV

Solution

1. Identify the given trigonometric ratio and the quadrant. In Quadrant IV, the xcoordinate is positive and the ycoordinate is negative.

2. Determine the side lengths of a reference triangle. Since cos(x)=adjacent/hypotenuse let the adjacent side a=4 and the hypotenuse h=5

3. Calculate the opposite side b using the Pythagorean theorem a2+b2=h2

4+b2=5

16+b2=25

b2=9

b=±3

4. Assign the correct sign to the opposite side based on the quadrant. Since the angle is in Quadrant IV, the yvalue (opposite side) must be negative.

b=−3

5. Evaluate the remaining trigonometric functions using the values a=4 b=−3 and h=5

sin(x)=opposite/hypotenuse=−3/5

tan(x)=opposite/adjacent=−3/4

csc(x)=1/sin(x)=−5/3

sec(x)=1/cos(x)=5/4

cot(x)=1/tan(x)=−4/3

Final Answer

sin(x)=−3/5,tan(x)=−3/4,csc(x)=−5/3,sec(x)=5/4,cot(x)=−4/3

Want more problems? Check here!