Evaluating inverse trigonometric functions

0/1
Introduction
Lessons
  1. Application of the Cancellation Laws

    Introduction to Evaluating Inverse Trigonometric Functions

0/14
Examples
Lessons
  1. Understanding the Use of Inverse Trigonometric Functions

    Find the angles for each of the following diagrams.

    1. Evaluating inverse trigonometric functions
    2. Evaluating inverse trigonometric functions
  2. Find the angle for the following isosceles triangle.

    Evaluating inverse trigonometric functions
    1. Determining the Angles in Exact Values by Using Special Triangles

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

      1. Evaluating inverse trigonometric functions
      2. Evaluating inverse trigonometric functions
    2. Application of the Cancellation Laws

      Solve the following inverse trigonometric functions:

      1. sin(sin10.5)\sin (\sin^{-1} 0.5)
      2. cos1(cosπ4)\cos^{-1} (\cos \frac{\pi}{4})
      3. sin1(sin3π4)\sin^{-1} (\sin \frac{3\pi}{4})
    3. Solving Expressions With One Inverse Trigonometry

      Solve the following inverse trigonometric functions:

      1. cos112\cos^{-1} \frac{1}{2}
      2. sin112\sin^{-1} \frac{1}{2}
    4. Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

      Solve the following inverse trigonometric functions:

      1. sin(cos132)\sin (\cos^{-1} \frac{\sqrt 3}{2})
      2. cos(sin123)\cos (\sin^{-1} \frac{2}{3})
      3. cos(2tan12)\cos (2\tan^{-1} \sqrt 2)
      4. cos(sin1x)\cos (\sin^{-1} x)
    5. Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

      Solve the following inverse trigonometric functions:

      1. cos1(cos3π2)\cos^{-1} (\cos \frac{3\pi}{2})
      2. sin1(sin5π2)\sin^{-1} (\sin \frac{5\pi}{2})
    Free to Join!
    StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
    • Easily See Your Progress

      We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
    • Make Use of Our Learning Aids

      Last Viewed
      Practice Accuracy
      Suggested Tasks

      Get quick access to the topic you're currently learning.

      See how well your practice sessions are going over time.

      Stay on track with our daily recommendations.

    • Earn Achievements as You Learn

      Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
    • Create and Customize Your Avatar

      Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
    Topic Notes

    In this lesson, we will learn:

    • Application of the Cancellation Laws
    • Solving Expressions With One Inverse Trigonometry
    • Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry
    • Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

    Cancellation Laws:

    sin1(sinx)=x  \sin^{-1} (\sin x) = x\;, π2xπ2-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}

    sin(sin1x)=x  \sin (\sin^{-1} x) = x\;, 1x1-1 \leq x \leq 1

    cos1(cosx)=x  \cos^{-1} (\cos x) = x\;, 0xπ0 \leq x \leq \pi

    cos(cos1x)=x  \cos (\cos^{-1} x) = x\;, 1x1-1 \leq x \leq 1

    tan1(tanx)=x  \tan^{-1} (\tan x) = x\;, π2xπ2-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}

    tan(tan1x)=x  \tan (\tan^{-1} x) = x\;, -\infty < xx < \infty

    Trigonometric Identity:

    cos2θ=cos2θsin2θ\cos 2\theta = \cos^{2} \theta - \sin^{2} \theta