Question: If sin A = 3/5, what is the value of cos A?
Options:
4/5
3/5
5/4
1/2
Correct Answer: 4/5
Solution:
Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
If sin A = 3/5, what is the value of cos A?
Practice Questions
Q1
If sin A = 3/5, what is the value of cos A?
4/5
3/5
5/4
1/2
Questions & Step-by-Step Solutions
If sin A = 3/5, what is the value of cos A?
Step 1: Start with the given value of sin A, which is 3/5.
Step 2: Use the Pythagorean identity, which states that sin^2 A + cos^2 A = 1.
Step 3: Calculate sin^2 A by squaring 3/5. This gives (3/5)^2 = 9/25.
Step 4: Substitute sin^2 A into the identity: 9/25 + cos^2 A = 1.
Step 5: To find cos^2 A, rearrange the equation: cos^2 A = 1 - 9/25.
Step 6: Convert 1 into a fraction with a denominator of 25: 1 = 25/25.
Step 7: Now subtract: cos^2 A = 25/25 - 9/25 = 16/25.
Step 8: To find cos A, take the square root of cos^2 A: cos A = sqrt(16/25).
Step 9: Calculate the square root: cos A = 4/5.
Trigonometric Identities – Understanding and applying the Pythagorean identity sin^2 A + cos^2 A = 1 to find the cosine of an angle when the sine is known.
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