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If cot(x) = 5/12, what is sin(x)?
If cot(x) = 5/12, what is sin(x)?
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Practice Questions
1 question
Q1
If cot(x) = 5/12, what is sin(x)?
12/13
5/13
13/12
5/12
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Using the identity cot(x) = cos(x)/sin(x), we can find sin(x) = 12/13 using the Pythagorean theorem.
Questions & Step-by-step Solutions
1 item
Q
Q: If cot(x) = 5/12, what is sin(x)?
Solution:
Using the identity cot(x) = cos(x)/sin(x), we can find sin(x) = 12/13 using the Pythagorean theorem.
Steps: 8
Show Steps
Step 1: Understand that cot(x) is the ratio of cos(x) to sin(x). So, cot(x) = cos(x) / sin(x).
Step 2: Given cot(x) = 5/12, we can write this as cos(x) / sin(x) = 5/12.
Step 3: Let sin(x) = 12k and cos(x) = 5k for some value k. This keeps the ratio the same.
Step 4: Use the Pythagorean theorem, which states that sin^2(x) + cos^2(x) = 1.
Step 5: Substitute sin(x) and cos(x) into the equation: (12k)^2 + (5k)^2 = 1.
Step 6: Simplify the equation: 144k^2 + 25k^2 = 1, which gives 169k^2 = 1.
Step 7: Solve for k: k^2 = 1/169, so k = 1/13.
Step 8: Now find sin(x): sin(x) = 12k = 12 * (1/13) = 12/13.
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