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If tan(x) = 3/4, what is the value of sin(x)?
If tan(x) = 3/4, what is the value of sin(x)?
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Q1
If tan(x) = 3/4, what is the value of sin(x)?
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Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after calculating the hypotenuse using the Pythagorean theorem.
Questions & Step-by-step Solutions
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Q: If tan(x) = 3/4, what is the value of sin(x)?
Solution:
Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after calculating the hypotenuse using the Pythagorean theorem.
Steps: 7
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Step 1: Understand that tan(x) = sin(x) / cos(x). We are given that tan(x) = 3/4.
Step 2: This means that sin(x) = 3k and cos(x) = 4k for some value k.
Step 3: Use the Pythagorean theorem to find the hypotenuse. The formula is sin^2(x) + cos^2(x) = 1.
Step 4: Substitute sin(x) and cos(x) into the equation: (3k)^2 + (4k)^2 = 1.
Step 5: Simplify the equation: 9k^2 + 16k^2 = 1, which gives 25k^2 = 1.
Step 6: Solve for k: k^2 = 1/25, so k = 1/5.
Step 7: Now find sin(x): sin(x) = 3k = 3 * (1/5) = 3/5.
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