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If sin θ = 0.8, what is the value of cos θ?
If sin θ = 0.8, what is the value of cos θ?
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Practice Questions
1 question
Q1
If sin θ = 0.8, what is the value of cos θ?
0.6
0.8
0.4
0.2
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Using the Pythagorean identity, cos θ = √(1 - sin²θ) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin θ = 0.8, what is the value of cos θ?
Solution:
Using the Pythagorean identity, cos θ = √(1 - sin²θ) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.
Steps: 8
Show Steps
Step 1: Start with the given value of sin θ, which is 0.8.
Step 2: Use the Pythagorean identity, which states that sin²θ + cos²θ = 1.
Step 3: Rearrange the identity to find cos²θ: cos²θ = 1 - sin²θ.
Step 4: Calculate sin²θ: sin²θ = (0.8)² = 0.64.
Step 5: Substitute sin²θ into the equation: cos²θ = 1 - 0.64.
Step 6: Calculate 1 - 0.64: cos²θ = 0.36.
Step 7: Take the square root of both sides to find cos θ: cos θ = √(0.36).
Step 8: Calculate the square root: cos θ = 0.6.
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