Find the Other Trig Values in Quadrant I cot(x)=5/12

Problem

cot(x)=5/12,0<x<π/2

Solution

1. Identify the given trigonometric ratio and the quadrant. Since cot(x)=5/12 and x is in Quadrant I, all trigonometric functions will be positive.

2. Define the relationship between the cotangent and the sides of a right triangle.

cot(x)=adjacent/opposite=5/12

3. Assign values to the adjacent side a and the opposite side o

a=5

o=12

4. Calculate the hypotenuse h using the Pythagorean theorem a2+o2=h2

5+12=h2

25+144=h2

169=h2

h=13

5. Determine the remaining trigonometric ratios using the values a=5 o=12 and h=13

sin(x)=o/h=12/13

cos(x)=a/h=5/13

tan(x)=o/a=12/5

csc(x)=h/o=13/12

sec(x)=h/a=13/5

Final Answer

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

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