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If sin(θ) = 3/5, what is cos(θ)?
If sin(θ) = 3/5, what is cos(θ)?
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Practice Questions
1 question
Q1
If sin(θ) = 3/5, what is cos(θ)?
4/5
3/5
5/4
1/5
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Using the Pythagorean identity, cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = 4/5.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(θ) = 3/5, what is cos(θ)?
Solution:
Using the Pythagorean identity, cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = 4/5.
Steps: 10
Show Steps
Step 1: Start with the given information: sin(θ) = 3/5.
Step 2: Recall the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
Step 3: Substitute sin(θ) into the identity: (3/5)² + cos²(θ) = 1.
Step 4: Calculate (3/5)²: (3/5)² = 9/25.
Step 5: Replace sin²(θ) in the equation: 9/25 + cos²(θ) = 1.
Step 6: To isolate cos²(θ), subtract 9/25 from both sides: cos²(θ) = 1 - 9/25.
Step 7: Convert 1 to a fraction with a denominator of 25: 1 = 25/25.
Step 8: Now, subtract: cos²(θ) = 25/25 - 9/25 = 16/25.
Step 9: Take the square root of both sides to find cos(θ): cos(θ) = √(16/25).
Step 10: Simplify the square root: cos(θ) = 4/5.
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