Find the Other Trig Values in Quadrant I tan(theta)=8/15

Problem

tan(θ)=8/15,0<θ<π/2

Solution

1. Identify the given values for the right triangle. Since tan(θ)=opposite/adjacent let the opposite side y=8 and the adjacent side x=15

2. Calculate the hypotenuse r using the Pythagorean theorem r2=x2+y2

r=√(,15+8)

r=√(,225+64)

r=√(,289)

r=17

3. Determine the sine and cosine values using the ratios sin(θ)=y/r and cos(θ)=x/r Since the angle is in Quadrant I, all trigonometric values are positive.

sin(θ)=8/17

cos(θ)=15/17

4. Find the reciprocal trigonometric functions by inverting the primary ratios.

csc(θ)=1/sin(θ)=17/8

sec(θ)=1/cos(θ)=17/15

cot(θ)=1/tan(θ)=15/8

Final Answer

sin(θ)=8/17,cos(θ)=15/17,csc(θ)=17/8,sec(θ)=17/15,cot(θ)=15/8

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