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If tan(θ) = 3/4, what is the value of sin(θ)?
If tan(θ) = 3/4, what is the value of sin(θ)?
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Q1
If tan(θ) = 3/4, what is the value of sin(θ)?
3/5
4/5
5/5
1
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Using the identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = 3/5.
Questions & Step-by-step Solutions
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Q
Q: If tan(θ) = 3/4, what is the value of sin(θ)?
Solution:
Using the identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = 3/5.
Steps: 6
Show Steps
Step 1: Understand that tan(θ) = opposite/adjacent. Here, tan(θ) = 3/4 means the opposite side is 3 and the adjacent side is 4.
Step 2: Use the Pythagorean theorem to find the hypotenuse. The formula is hypotenuse² = opposite² + adjacent².
Step 3: Calculate the hypotenuse: hypotenuse² = 3² + 4² = 9 + 16 = 25.
Step 4: Find the hypotenuse by taking the square root: hypotenuse = √25 = 5.
Step 5: Now, use the definition of sin(θ) = opposite/hypotenuse. Here, sin(θ) = 3/5.
Step 6: Therefore, the value of sin(θ) is 3/5.
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