Find the Other Trig Values in Quadrant I tan(theta)=3/4

Problem

tan(θ)=3/4,θ∈Quadrant I

Solution

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

opposite=3

adjacent=4

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

3+4=c2

9+16=c2

25=c2

c=5

3. Determine the sine and cosine values using the ratios sin(θ)=opposite/hypotenuse and cos(θ)=adjacent/hypotenuse Since θ is in Quadrant I, all values are positive.

sin(θ)=3/5

cos(θ)=4/5

4. Find the reciprocal trigonometric values by inverting the sine, cosine, and tangent ratios.

csc(θ)=5/3

sec(θ)=5/4

cot(θ)=4/3

Final Answer

sin(θ)=3/5,cos(θ)=4/5,csc(θ)=5/3,sec(θ)=5/4,cot(θ)=4/3

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