Find the Other Trig Values in Quadrant I tan(x)=60/11

Problem

tan(x)=60/11, Quadrant I

Solution

1. Identify the components of the tangent function. Since tan(x)=opposite/adjacent we let the opposite side a=60 and the adjacent side b=11

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

60+11=c2

3600+121=c2

3721=c2

c=√(,3721)=61

3. Determine the signs of the trigonometric functions. In Quadrant I, all trigonometric values (sine, cosine, tangent, cosecant, secant, and cotangent) are positive.

4. Evaluate the sine and cosecant functions using the ratios sin(x)=opposite/hypotenuse and csc(x)=1/sin(x)

sin(x)=60/61

csc(x)=61/60

5. Evaluate the cosine and secant functions using the ratios cos(x)=adjacent/hypotenuse and sec(x)=1/cos(x)

cos(x)=11/61

sec(x)=61/11

6. Evaluate the cotangent function using the ratio cot(x)=1/tan(x)

cot(x)=11/60

Final Answer

sin(x)=60/61,cos(x)=11/61,csc(x)=61/60,sec(x)=61/11,cot(x)=11/60

Want more problems? Check here!