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If sin(θ) = 0.8, what is cos(θ)? (2022)
If sin(θ) = 0.8, what is cos(θ)? (2022)
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Practice Questions
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Q1
If sin(θ) = 0.8, what is cos(θ)? (2022)
0.6
0.8
0.4
0.2
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Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(θ) = 0.8, what is cos(θ)? (2022)
Solution:
Using sin²(θ) + cos²(θ) = 1, cos(θ) = √(1 - 0.8²) = √(0.36) = 0.6.
Steps: 8
Show Steps
Step 1: Start with the given information: sin(θ) = 0.8.
Step 2: Recall the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
Step 3: Calculate sin²(θ): 0.8² = 0.64.
Step 4: Substitute sin²(θ) into the identity: 0.64 + cos²(θ) = 1.
Step 5: Rearrange the equation to find cos²(θ): cos²(θ) = 1 - 0.64.
Step 6: Calculate 1 - 0.64: cos²(θ) = 0.36.
Step 7: Take the square root to find cos(θ): cos(θ) = √(0.36).
Step 8: Calculate the square root: cos(θ) = 0.6.
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