Evaluating inverse trigonometric functions

Lessons

• Introduction
  Application of the Cancellation Laws

  Introduction to Evaluating Inverse Trigonometric Functions

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• 1.
  Understanding the Use of Inverse Trigonometric Functions

  Find the angles for each of the following diagrams.

  a)

  
  
  
  b)

  
  
  

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• 2.

  Find the angle for the following isosceles triangle.

  

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• 3.
  Determining the Angles in Exact Values by Using Special Triangles

  Find the angles for each of the following diagrams in exact value.

  a)

  
  
  
  b)

  
  
  

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• 4.
  Application of the Cancellation Laws

  Solve the following inverse trigonometric functions:

  a)

  $\sin (\sin^{-1} 0.5)$
  
  
  b)

  $\cos^{-1} (\cos \frac{\pi}{4})$
  
  
  c)

  $\sin^{-1} (\sin \frac{3\pi}{4})$
  
  

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• 5.
  Solving Expressions With One Inverse Trigonometry

  Solve the following inverse trigonometric functions:

  a)

  $\cos^{-1} \frac{1}{2}$
  
  
  b)

  $\sin^{-1} \frac{1}{2}$
  
  

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• 6.
  Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

  Solve the following inverse trigonometric functions:

  a)

  $\sin (\cos^{-1} \frac{\sqrt 3}{2})$
  
  
  b)

  $\cos (\sin^{-1} \frac{2}{3})$
  
  
  c)

  $\cos (2\tan^{-1} \sqrt 2)$
  
  
  d)

  $\cos (\sin^{-1} x)$
  
  

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• 7.
  Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

  Solve the following inverse trigonometric functions:

  a)

  $\cos^{-1} (\cos \frac{3\pi}{2})$
  
  
  b)

  $\sin^{-1} (\sin \frac{5\pi}{2})$
  
  

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