Evaluating the Composition of a Trigonometric Function and Its Inverse (6.7.4)

Question 1

• To evaluate a composite trigonometric function:
  
  • First find the value of the inner expression.
  • Then evaluate the outer expression (usually an inverse) at that value.

Answer 1

• To evaluate a composite trigonometric function:
  
  • First find the value of the inner expression.
  • Then evaluate the outer expression (usually an inverse) at that value.

Question 2

• Always consider the range of the inverses. Certain answers are not allowed when solving an inverse trig function.
  
  • The range of sin^-1x is the interval [-π/2, π/2].
  • The range of cos^-1x is the interval [0, π].
  • The range of tan^-1x is the interval (-π/2, π/2)

Answer 2

• Always consider the range of the inverses. Certain answers are not allowed when solving an inverse trig function.
  
  • The range of sin^-1x is the interval [-π/2, π/2].
  • The range of cos^-1 x is the interval [0, π].
  • The range of tan^-1 x is the interval (-π/2, π/2)