If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?
Practice Questions
Q1
If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?
0.8
0.6
0.4
0.2
Questions & Step-by-Step Solutions
If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?
Step 1: Start with the given value of sin(θ), which is 0.6.
Step 2: Use the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
Step 3: Calculate sin²(θ) by squaring the value of sin(θ): 0.6 * 0.6 = 0.36.
Step 4: Substitute sin²(θ) into the Pythagorean identity: 0.36 + cos²(θ) = 1.
Step 5: Rearrange the equation to solve for cos²(θ): cos²(θ) = 1 - 0.36.
Step 6: Calculate 1 - 0.36, which equals 0.64.
Step 7: Take the square root of cos²(θ) to find cos(θ): cos(θ) = √0.64.
Step 8: Calculate the square root of 0.64, which is 0.8.
Pythagorean Identity – The relationship between sine and cosine, expressed as sin²(θ) + cos²(θ) = 1, which allows for the calculation of one function when the other is known.
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