Find the Other Trig Values in Quadrant I tan(x)=7/24

Problem

tan(x)=7/24,0<x<π/2

Solution

1. Identify the given information and the quadrant. Since x is in Quadrant I, all trigonometric ratios (sin(x) cos(x) tan(x) csc(x) sec(x) cot(x) are positive.

2. Define the sides of a right triangle using the definition tan(x)=opposite/adjacent Let the opposite side a=7 and the adjacent side b=24

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

7+24=c2

49+576=c2

625=c2

c=25

4. Determine the sine and cosine values using the ratios sin(x)=opposite/hypotenuse and cos(x)=adjacent/hypotenuse

sin(x)=7/25

cos(x)=24/25

5. Find the reciprocal identities for the remaining trigonometric functions.

csc(x)=1/sin(x)=25/7

sec(x)=1/cos(x)=25/24

cot(x)=1/tan(x)=24/7

Final Answer

sin(x)=7/25,cos(x)=24/25,csc(x)=25/7,sec(x)=25/24,cot(x)=24/7

Want more problems? Check here!