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

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

Step 1: Understand that cot θ = 3/4 means that the ratio of cos θ to sin θ is 3/4.
Step 2: Write cot θ as cos θ / sin θ, so we have cos θ / sin θ = 3/4.
Step 3: Let sin θ = 4k and cos θ = 3k for some value k, since the ratio is 3:4.
Step 4: Use the Pythagorean identity sin² θ + cos² θ = 1.
Step 5: Substitute sin θ and cos θ into the identity: (4k)² + (3k)² = 1.
Step 6: Calculate (16k²) + (9k²) = 1, which simplifies to 25k² = 1.
Step 7: Solve for k by dividing both sides by 25: k² = 1/25, so k = 1/5.
Step 8: Now find sin θ: sin θ = 4k = 4 * (1/5) = 4/5.

Trigonometric Identities – Understanding the relationship between cotangent, sine, and cosine.
Pythagorean Theorem – Using the identity sin²θ + cos²θ = 1 to find the values of sine and cosine.