Find the Other Trig Values in Quadrant I sin(x)=5/13

Problem

sin(x)=5/13, Quadrant I

Solution

1. Identify the given values for the right triangle. Since sin(x)=opposite/hypotenuse we have y=5 and r=13

2. Apply the Pythagorean theorem x2+y2=r2 to find the adjacent side x

x2+5=13

x2+25=169

x2=144

x=12

Note that x is positive because the angle is in Quadrant I.

3. Determine the cosine value using cos(x)=x/r

cos(x)=12/13

4. Determine the tangent value using tan(x)=y/x

tan(x)=5/12

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

csc(x)=13/5

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

sec(x)=13/12

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

cot(x)=12/5

Final Answer

cos(x)=12/13,tan(x)=5/12,csc(x)=13/5,sec(x)=13/12,cot(x)=12/5

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