Mathematical Scratchpad

Review for final

  1. Describe how you can find the relationship among three sides of a right triangle when the angles are MATH and $90^{\circ }.$

  2. For MATH Find (a) $\sin \theta $ (b) $\cos \theta .$

  3. If MATH and MATH Find $(a)\cos (\pi -t),$ $(b)\cot (\pi -t)..$

  4. $f(x)=-\sqrt{x-2}.$ Find the inverse function for $f$ if it exists. If they exist, graph $y=f(x)$ and $y=f^{-1}(x)$ together.

  5. If the graph of $y=f(x)$ is shown below:
    finalreview__15.png

    1. Sketch the graph of $y=-f(x).$

    2. Sketch the graph of $y=f(-x).$

    3. Sketch the graph of MATH

    4. Sketch the graph of MATH

  6. If $f(x)=\cos ^{-1}x$ or $\arccos (x).$ Then

    1. find the domain and range for $f.$

    2. sketch the graph of $f.$

  7. If $f(x)=\sin ^{-1}x$ or $\arcsin (x).$ Then

    1. find the domain and range for $f.$

    2. sketch the graph of $f.$

  8. If $f(x)=\tan ^{-1}x.$ Then

    1. find the domain and range for $f.$

    2. sketch the graph of $f.$

  9. If MATHfind the inverse functions for $f(x+\pi )$ and $f(x)+\pi $ respectively.

  10. If MATHfind the inverse functions for $f(x+\pi )$ and $f(x)+\pi $ respectively.

  11. Find the exact vaule of the expression without using a calculator

    1. MATH

    2. MATH

    3. MATH

    4. MATH

    5. MATH

  12. Write an algebraic expression that is equivalent to the given expression.

    1. MATH

    2. MATH

  13. Prove the followings graphically:

    1. MATH

    2. MATH

    3. $\sin (-x)=-\sin x$

    4. $\cos (-x)=\cos x$

  14. Prove MATH algebraically.

  15. Prove MATH algebraically.

  16. Prove MATH

  17. If the graph of $y=\sec (x)$ is given, then

    1. find the vertical asymptotes for MATH

    2. sketch MATH by changing the units from $y=\sec (x). $

  18. Simplify the following expressions algebraically first and prove your results graphically with explanations

    1. MATH

    2. MATH

    3. MATH

  19. page 221, 81-88. Trig substitutions.

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