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If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)

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Question: If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)

Options:

  1. 0.4
  2. 0.5
  3. 0.6
  4. 0.8

Correct Answer: 0.4

Exam Year: 2017

Solution: 

sin²(θ) + cos²(θ) = 1; sin²(θ) = 1 - 0.6² = 0.64; sin(θ) = √0.64 = 0.8.

If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)

Practice Questions

Q1
If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)
  1. 0.4
  2. 0.5
  3. 0.6
  4. 0.8

Questions & Step-by-Step Solutions

If cos(θ) = 0.6, what is sin(θ) using Pythagorean identity? (2017)
  • Step 1: Start with the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
  • Step 2: Substitute the value of cos(θ) into the equation: sin²(θ) + (0.6)² = 1.
  • Step 3: Calculate (0.6)²: 0.6 * 0.6 = 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: sin²(θ) = 0.64.
  • Step 7: To find sin(θ), take the square root of 0.64: sin(θ) = √0.64.
  • Step 8: Calculate √0.64: sin(θ) = 0.8.
  • Pythagorean Identity – The relationship between sine and cosine functions, expressed as sin²(θ) + cos²(θ) = 1.
  • Square Root Calculation – Understanding how to take the square root of a number and the implications of positive and negative roots.
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