Find the Exact Value sin(arctan(3/4))

Problem

sin(arctan(3/4))

Solution

1. Identify the inner expression as an angle θ=arctan(3/4) which implies tan(θ)=3/4

2. Visualize a right triangle where the side opposite to θ is 3 and the side adjacent to θ is 4

3. Apply the Pythagorean theorem to find the hypotenuse h of the triangle.

h=√(,3+4)

h=√(,9+16)

h=√(,25)

h=5

4. Determine the value of sin(θ) using the ratio of the opposite side to the hypotenuse.

sin(θ)=opposite/hypotenuse

sin(θ)=3/5

Final Answer

sin(arctan(3/4))=3/5

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