Find the Other Trig Values in Quadrant I sin(x)=3/5

Problem

sin(x)=3/5, Quadrant I

Solution

1. Identify the given values for the right triangle. Since sin(x)=opposite/hypotenuse we have y=3 and r=5

2. Apply the Pythagorean theorem to find the adjacent side x In Quadrant I, both x and y are positive.

x2+y2=r2

x2+3=5

x2+9=25

x2=16

x=4

3. Determine the cosine value using the ratio cos(x)=adjacent/hypotenuse

cos(x)=4/5

4. Determine the tangent value using the ratio tan(x)=opposite/adjacent

tan(x)=3/4

5. Determine the reciprocal identities for cosecant, secant, and cotangent.

csc(x)=1/sin(x)=5/3

sec(x)=1/cos(x)=5/4

cot(x)=1/tan(x)=4/3

Final Answer

cos(x)=4/5,tan(x)=3/4,csc(x)=5/3,sec(x)=5/4,cot(x)=4/3

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