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

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

Step 1: Understand that cot A is the ratio of cos A to sin A. Here, cot A = 3/4 means cos A/sin A = 3/4.
Step 2: Let sin A = y and cos A = x. From cot A = 3/4, we can write x/y = 3/4.
Step 3: Rearrange the equation to express x in terms of y: x = (3/4)y.
Step 4: Use the Pythagorean identity sin²A + cos²A = 1. Substitute x and y: y² + ((3/4)y)² = 1.
Step 5: Simplify the equation: y² + (9/16)y² = 1, which gives (25/16)y² = 1.
Step 6: Solve for y²: y² = 16/25, so y = √(16/25) = 4/5.
Step 7: Since y represents sin A, we find that sin A = 4/5.

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