If tan A = 3/4, what is the value of sin A?

If tan A = 3/4, what is the value of sin A?

Step 1: Understand that tan A = sin A / cos A. This means that the tangent of angle A is the ratio of the sine of angle A to the cosine of angle A.
Step 2: We know that tan A = 3/4. This means sin A / cos A = 3/4.
Step 3: Let's represent sin A as 3k and cos A as 4k for some value k. This keeps the ratio the same: (3k)/(4k) = 3/4.
Step 4: Now, we use the Pythagorean identity: sin² A + cos² A = 1.
Step 5: Substitute sin A and cos A: (3k)² + (4k)² = 1.
Step 6: Calculate: 9k² + 16k² = 1, which simplifies to 25k² = 1.
Step 7: Solve for k²: k² = 1/25, so k = 1/5.
Step 8: Now, find sin A: sin A = 3k = 3 * (1/5) = 3/5.

Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent functions.
Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find the values of sine and cosine.