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If cot A = 3/4, what is the value of sin A?

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Question: If cot A = 3/4, what is the value of sin A?

Options:

  1. 3/5
  2. 4/5
  3. 5/3
  4. 5/4

Correct Answer: 3/5

Solution: 

cot A = cos A/sin A = 3/4 implies sin A = 4/5 using the identity sin²A + cos²A = 1.

If cot A = 3/4, what is the value of sin A?

Practice Questions

Q1
If cot A = 3/4, what is the value of sin A?
  1. 3/5
  2. 4/5
  3. 5/3
  4. 5/4

Questions & Step-by-Step Solutions

If cot A = 3/4, what is the value of sin A?
  • Step 1: Understand that cot A is the ratio of cos A to sin A. Here, cot A = 3/4 means cos A/sin A = 3/4.
  • Step 2: Let sin A = y and cos A = x. From cot A = 3/4, we can write x/y = 3/4.
  • Step 3: Rearrange the equation to express x in terms of y: x = (3/4)y.
  • Step 4: Use the Pythagorean identity sin²A + cos²A = 1. Substitute x and y: y² + ((3/4)y)² = 1.
  • Step 5: Simplify the equation: y² + (9/16)y² = 1, which gives (25/16)y² = 1.
  • Step 6: Solve for y²: y² = 16/25, so y = √(16/25) = 4/5.
  • Step 7: Since y represents sin A, we find that sin A = 4/5.
  • Trigonometric Identities – Understanding the relationship between cotangent, sine, and cosine, and how to use the Pythagorean identity.
  • Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find the values of sine and cosine from cotangent.
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