Half-Angle: Formulas & Proof


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question 1 of 3

What is tan θ in the following figure?

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1. In the following figure, what is sin θ/2 ?

2. We are looking for a correct formula(s) relating θ/2 to θ in the following figure? Choose the best possible answer.

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About This Quiz & Worksheet

Find the measure of angles in a triangle with half-angle formulas for sine, cosine and tangent. Answer questions about the tangent ratio and the half-angle formula for sine.

Quiz & Worksheet Goals

These practice questions test your ability to:

  • Find basic trigonometric ratios
  • Calculate the measure of an angle given a figure
  • Choose the correct formula to relate theta and (theta/2)

Skills Practiced

  • Problem solving - apply the half-angle formula for sine to a practice problem
  • Distinguishing differences - determine the correct half-angle formula to use to find the measure of theta
  • Knowledge application - use what you know about trigonometric formulas to find angle measures within a given triangle

Additional Learning

Read more about using half-angle formulas correctly in the lesson entitled Half-Angle: Formulas & Proof. The lesson gives you information about:

  • Types of angles and the Greek letter theta
  • Three theorems that form the basis for the half-angle formulas
  • How half-angle formulas are related to Pythagoras' Theorem
  • Three options for the half-angle formula for tangent