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If tan(θ) = 1, what is the value of θ in degrees?

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Question: If tan(θ) = 1, what is the value of θ in degrees?

Options:

  1. 30
  2. 45
  3. 60
  4. 90

Correct Answer: 45

Solution: 

tan(θ) = 1 at θ = 45°.

If tan(θ) = 1, what is the value of θ in degrees?

Practice Questions

Q1
If tan(θ) = 1, what is the value of θ in degrees?
  1. 30
  2. 45
  3. 60
  4. 90

Questions & Step-by-Step Solutions

If tan(θ) = 1, what is the value of θ in degrees?
  • Step 1: Understand that tan(θ) represents the tangent of an angle θ.
  • Step 2: Recall that the tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.
  • Step 3: Recognize that tan(θ) = 1 means the opposite side and the adjacent side are equal in length.
  • Step 4: Identify the angle where the opposite and adjacent sides are equal. This occurs at 45° in a right triangle.
  • Step 5: Conclude that if tan(θ) = 1, then θ must be 45°.
  • Trigonometric Functions – Understanding the properties and values of trigonometric functions, specifically the tangent function.
  • Angle Measurement – Knowledge of angle measurement in degrees and the specific angles where trigonometric functions yield certain values.
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