If tan(θ) = 3/4, what is the value of sin(θ)?

If tan(θ) = 3/4, what is the value of sin(θ)?

Correct Answer: 3/5

Step 1: Understand that tan(θ) = opposite/adjacent. Here, tan(θ) = 3/4 means the opposite side is 3 and the adjacent side is 4.
Step 2: Use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse² = opposite² + adjacent².
Step 3: Calculate the hypotenuse: hypotenuse² = 3² + 4² = 9 + 16 = 25.
Step 4: Find the hypotenuse by taking the square root: hypotenuse = √25 = 5.
Step 5: Now, use the definition of sin(θ) = opposite/hypotenuse. Here, sin(θ) = 3/5.
Step 6: Therefore, the value of sin(θ) is 3/5.

Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent through the Pythagorean identity.
Right Triangle Ratios – Using the definition of tangent as the ratio of opposite to adjacent sides in a right triangle.