Find the Other Trig Values in Quadrant I sin(x)=4/7

Problem

sin(x)=4/7,x∈Quadrant I

Solution

1. Identify the given trigonometric ratio and the quadrant. In Quadrant I, all trigonometric functions (sin() cos() tan() csc() sec() cot() are positive.

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

(4/7)2+cos2(x)=1

16/49+cos2(x)=1

cos2(x)=1−16/49

cos2(x)=33/49

cos(x)=√(,33/49)

cos(x)=√(,33)/7

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

tan(x)=(4/7)/(√(,33)/7)

tan(x)=4/√(,33)

tan(x)=(4√(,33))/33

4. Find the reciprocal functions csc(x) sec(x) and cot(x) by inverting the primary ratios.

csc(x)=1/sin(x)=7/4

sec(x)=1/cos(x)=7/√(,33)=(7√(,33))/33

cot(x)=1/tan(x)=√(,33)/4

Final Answer

cos(x)=√(,33)/7,tan(x)=(4√(,33))/33,csc(x)=7/4,sec(x)=(7√(,33))/33,cot(x)=√(,33)/4

Want more problems? Check here!