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

Problem

tan(x)=15/8, Quadrant I

Solution

1. Identify the components of the tangent function using the ratio of sides in a right triangle, where tan(x)=opposite/adjacent

opposite=15

adjacent=8

2. Apply the Pythagorean theorem to find the hypotenuse r using the formula r=√(,opposite2+adjacent2)

r=√(,15+8)

r=√(,225+64)

r=√(,289)

r=17

3. Determine the signs of the trigonometric functions based on the given location. Since x is in Quadrant I, all trigonometric values (sine, cosine, tangent, cosecant, secant, and cotangent) are positive.

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

sin(x)=15/17

cos(x)=8/17

5. Evaluate the reciprocal functions using the ratios csc(x)=1/sin(x) sec(x)=1/cos(x) and cot(x)=1/tan(x)

csc(x)=17/15

sec(x)=17/8

cot(x)=8/15

Final Answer

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

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