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If cot θ = 3/4, what is the value of sin θ?
If cot θ = 3/4, what is the value of sin θ?
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Practice Questions
1 question
Q1
If cot θ = 3/4, what is the value of sin θ?
4/5
3/5
5/4
3/4
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Using the identity cot θ = cos θ / sin θ, we find sin θ = 4/5.
Questions & Step-by-step Solutions
1 item
Q
Q: If cot θ = 3/4, what is the value of sin θ?
Solution:
Using the identity cot θ = cos θ / sin θ, we find sin θ = 4/5.
Steps: 8
Show Steps
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.
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