Download Precalculus Practice with Trigonometric Functions of Real Numbers

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Precalculus Practice with Trigonometric Functions of Real Numbers
1. State the reciprocal relationships that exist between the six trigonometric functions.
2. In what quadrants are the sine function (and its reciprocal) positive? Negative?
3. In what quadrants are the cosine function (and its reciprocal) positive? Negative?
4. In what quadrants are the tangent function (and its reciprocal) positive? Negative?
In problems 5-10, determine the point P(x,y) on the unit circle that corresponds to the given number x, then
determine the value of sin x, cos x, tan x, csc x, sec x, cot x. If no such value exists, state that the value DNE.
x  2
6. x 
3
2
7. x 
9
4
9. x 
7
3
10. x 
13
4
11. x  7
12. x 

6
13. x 
14
3
5.
8. x 
2
3
s
, can be used to measure arc length along a circle. Specifically, for a circle
r
of radius r, a central angle  intercepts an arc of length s given by s = r  where  is measured in radians.
The radian measure formula,  
14. A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240  .
(remember to change from degree to radian measure)
The formula for the length of a circular arc can be used to analyze the motion of a particle moving at a constant
speed along a circular path. If s is the length of the arc traveled in time t, the speed of the particle is
dis tan ce s
Speed 

time
t
15. The second hand of a clock is 10.2 centimeters long. Find the speed of the tip of this second hand.
(hints: time for one revolution is 60 seconds, distance is the circumference)
Determine two coterminal angles for each of the following.
16.
2
3
17.
3
4
18.

8
19.
4
7
20.
13
3
21.
2
15
22.

2
23.
11
6
For each of the problems above (16-23) determine the quadrant in which the angle lies.
(you may write the answers above, by the problem)


) and then find cos (
). (hint: check the mode on your calculator) Thinking
6
6
back to your definition of even and odd functions, is the cosine function even or odd? Perform the same test for
sine and determine if the sine function is an even or odd function. What about tangent? Explain your results
below.
24. On a calculator, find cos (