Find the Other Trig Values in Quadrant I tan(x)=3/7

Problem

tan(x)=3/7,0<x<π/2

Solution

1. Identify the given ratio and the quadrant. Since tan(x)=opposite/adjacent=3/7 and x is in Quadrant I, both the opposite side a=3 and the adjacent side b=7 are positive.

2. Calculate the hypotenuse c using the Pythagorean theorem a2+b2=c2

3+7=c2

9+49=c2

c=√(,58)

3. Determine the sine value using the ratio sin(x)=opposite/hypotenuse

sin(x)=3/√(,58)

sin(x)=(3√(,58))/58

4. Determine the cosine value using the ratio cos(x)=adjacent/hypotenuse

cos(x)=7/√(,58)

cos(x)=(7√(,58))/58

5. Determine the cosecant value by taking the reciprocal of the sine.

csc(x)=√(,58)/3

6. Determine the secant value by taking the reciprocal of the cosine.

sec(x)=√(,58)/7

7. Determine the cotangent value by taking the reciprocal of the tangent.

cot(x)=7/3

Final Answer

sin(x)=(3√(,58))/58,cos(x)=(7√(,58))/58,csc(x)=√(,58)/3,sec(x)=√(,58)/7,cot(x)=7/3

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