If cos(θ) = 0.6, what is sin(θ) using the Pythagorean identity?

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Question: If cos(θ) = 0.6, what is sin(θ) using the Pythagorean identity?

Options:

Correct Answer: 0.8

Solution:

Using sin²θ + cos²θ = 1, sin²θ = 1 - 0.6² = 0.64, so sin(θ) = 0.8.

If cos(θ) = 0.6, what is sin(θ) using the Pythagorean identity?

If cos(θ) = 0.6, what is sin(θ) using the Pythagorean identity?

Step 1: Start with the Pythagorean identity, which states that sin²(θ) + cos²(θ) = 1.
Step 2: We know that cos(θ) = 0.6, so we can substitute this value into the identity: sin²(θ) + (0.6)² = 1.
Step 3: Calculate (0.6)², which is 0.36.
Step 4: Now the equation looks like this: sin²(θ) + 0.36 = 1.
Step 5: To find sin²(θ), subtract 0.36 from 1: sin²(θ) = 1 - 0.36.
Step 6: Calculate 1 - 0.36, which equals 0.64.
Step 7: Now we have sin²(θ) = 0.64. To find sin(θ), take the square root of 0.64.
Step 8: The square root of 0.64 is 0.8, so sin(θ) = 0.8.

Pythagorean Identity – The relationship sin²(θ) + cos²(θ) = 1, which relates the sine and cosine of an angle.