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If cot θ = 5/12, what is the value of sin θ?
If cot θ = 5/12, what is the value of sin θ?
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Practice Questions
1 question
Q1
If cot θ = 5/12, what is the value of sin θ?
5/13
12/13
13/5
12/5
Show Solution
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Using the identity cot θ = cos θ / sin θ, we can find sin θ = 12/13 using the Pythagorean theorem: sin θ = 12/√(5^2 + 12^2) = 12/13.
Questions & Step-by-step Solutions
1 item
Q
Q: If cot θ = 5/12, what is the value of sin θ?
Solution:
Using the identity cot θ = cos θ / sin θ, we can find sin θ = 12/13 using the Pythagorean theorem: sin θ = 12/√(5^2 + 12^2) = 12/13.
Steps: 6
Show Steps
Step 1: Understand that cot θ = 5/12 means that the adjacent side is 5 and the opposite side is 12 in a right triangle.
Step 2: Use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse^2 = adjacent^2 + opposite^2.
Step 3: Calculate the hypotenuse: hypotenuse^2 = 5^2 + 12^2 = 25 + 144 = 169.
Step 4: Find the hypotenuse by taking the square root: hypotenuse = √169 = 13.
Step 5: Now, use the definition of sine: sin θ = opposite / hypotenuse.
Step 6: Substitute the values: sin θ = 12 / 13.
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