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I often hear my Calculus teaching colleagues complain about their

By Bernice Reynolds,2014-11-25 17:32
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I often hear my Calculus teaching colleagues complain about their

    Trigonometry Review Worksheet

    In this course, you will need to use some trigonometry. This worksheet is designed to remind you some of the concepts. You should be able to complete the worksheet without using a calculator. Show your work when you are completing these problems, and ask me in class if you encounter any questions.

    1. In Calculus, all angles are measured in radians. Convert each of the following radian measures into degrees:

    555a) b) c) 632

2. Now let’s work with some right triangles:

a) Find the length of the unmarked side:

    b) In Calculus, we tend to use variables more than numbers in our trigonometric expressions. Again, find the length of the unmarked side.

    3. In addition to working with the sides of a triangle, we also work with the angles.

a) For the triangle below, find cos(),sin(),tan(),sec(),csc() and cot(),,,,,,

b) While you’re at it, tan(),sec(),csc() and cot(),,,, can all be written in terms of cos() and sin(),,.

    Go ahead and do that.

    4. Sometimes you will know the value of one trigonometric function and need to compute the others. For this problem, suppose you know that . siny;;

    Find cos(),tan(),sec(),csc() and cot(),,,,,.

    5. You should also know the value of some trigonometric functions applied to special values.

a) Find each of the following:

    (a) (b) (c) cossintan;;;;;;324

    0,,xb) Solve each of the following for x: (with ) 2

    tan()1x(a)

    (b) sin()0x

    (c) cos()0x

    1cos()x(d) 2

    3(e) sin()x2

    22sin()xcos()x6. a) There is a useful identity involving and . State it:

    22sec()xtan()x b) There is another useful identify that involves and . What is it?

    22csc()xcot()x c) The third identity in this family involves and . What is this identity?

7. While we are on the subject of identities, you should be able to express each of the following in terms

    sin(),sin(),cos() and cos()xhxhof . Go ahead and do it.

    sin()xha)

    cos()xhb)

8. Of course right triangles are not the only kind of triangles. Use the law of cosines to find the length of

    the missing side:

9. As I’m sure you remember from your trigonometry class, and can be defined for any sin()xcos()x

    value of x. And once you’ve done this, you can graph them.

    a) What is the largest possible value of ? sin()x

    b) What is the largest possible value of ? cos()x

    c) Sketch the graph of . Label the interesting points. sin()x

    d) Sketch the graph of . Label the interesting points. cos()x

    10. The period of a function f is the smallest positive number L such that fxfxL()()?? for all x in the domain of f. In other words, for a function that endlessly repeats itself, the period is the length of the

    smallest cycle. Determine the periods of the following functions:

    sin()xa)

    cos()xb)

    tan()xc)

    sin(2)xd)

    e) sinsin(2)xx;;

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