Trigonometry Review Worksheet Name_______________________________________

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Trigonometry Review Worksheet Name_______________________________________
Trigonometry Review Worksheet
In this course, you will need to use some trigonometry. Rather than use class time to dredge up half forgotten
memories, you are going to remind yourself with this worksheet. You should be able to complete the worksheet
without using a calculator.
1. In Calculus, all angles are measured in radians. Convert each of the following radian measures into degrees:
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( )
Hint: You calculated the length of the unknown side in the previous problem.
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 sin    y .
Find cos( ), tan( ), sec( ), csc( ) and cot( ) .
Hint: Draw a triangle similar to the one in 3a.
5. You should also know the value of some trigonometric functions applied to special values.
a) Find each of the following:
cos  3  , sin  2  , tan  4 
b) Solve each of the following for x: (with 0  x 
tan( x)  1 , sin( x)  0 , cos( x)  0 , cos( x)  12 , sin( x) 
6. a) There is a useful identity involving sin 2 ( x) and cos 2 ( x) . State it.
b) There is another useful identify that involves sec 2 ( x) and tan 2 ( x) . What is it?
c) The third identity in this family involves csc2 ( x) and cot 2 ( x) . 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 of
sin( x), sin(h), cos( x) and cos(h) . Go ahead and do it.
a) sin( x  h)
b) cos( x  h)
8. Of course right triangles are not the only kinds 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, sin( x) and cos( x) can be defined for any 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 sin( x) . Label the interesting points.
d) Sketch the graph of cos( x) . Label the interesting points.
10. The period of a function f is the smallest positive number L such that f ( x)  f ( x  L) 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:
a) sin( x)
b) cos( x)
c) tan( x)
d) sin(2 x)
e) sin  x   sin(2 x)
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