Find the Other Trig Values in Quadrant I sin(x)=21/29

Problem

sin(x)=21/29, Quadrant I

Solution

1. Identify the given trigonometric ratio and the quadrant. In Quadrant I, all trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are positive.

2. Use the Pythagorean identity sin2(x)+cos2(x)=1 to find the value of cos(x)

(21/29)2+cos2(x)=1

3. Solve for cosine by squaring the fraction and subtracting it from 1.

441/841+cos2(x)=1

cos2(x)=1−441/841

cos2(x)=400/841

cos(x)=√(,400/841)

cos(x)=20/29

4. Calculate tangent using the identity tan(x)=sin(x)/cos(x)

tan(x)=(21/29)/(20/29)

tan(x)=21/20

5. Find the reciprocal identities for cosecant, secant, and cotangent.

csc(x)=1/sin(x)=29/21

sec(x)=1/cos(x)=29/20

cot(x)=1/tan(x)=20/21

Final Answer

cos(x)=20/29,tan(x)=21/20,csc(x)=29/21,sec(x)=29/20,cot(x)=20/21

Want more problems? Check here!