Download Trig Worksheet

Honors Geometry
Trig Worksheet
A.M.D.G.
Use your calculator to find the values of each of the following. Note any trends that you
find:
cos  60  
cos  60  
cos  420  
cos  420  
cos  300  
cos  300  
cos  780  
cos  660  
In which two quadrants are the values for the cosine of an angle the same? Verify this on
your unit circle.
sin  60  
sin 120  
sin  420  
sin  480  
sin  300  
sin  240  
In which two quadrants are the values for the cosine of an angle the same? Verify this on
your unit circle.
tan  45  
tan  225  
tan  405  
tan  135  
tan  315  
tan  585  
In which two quadrants are the values for the cosine of an angle the same? Verify this on
your unit circle.
These quadrant values lead us to certain conclusions – that is that when we take an
inverse trig function to find an angle, we get more than one answer when we deal with
angles as rotations.
Below are some rules for how to undo trig functions. These are extensions of what we
worked with earlier in the year, and they account for the fact that multiple angles can give
us the same values for the trig functions (calc. refers to the value that you get from your
calculator):
Degrees:
 x
cos 1    calc.  360 n
r
calc.  360 n
 y 
sin 1    
r 
180  calc.  360 n
 y
tan 1    calc.  180 n
x
Radians:
 x
cos 1    calc.  2 n
r
calc.  2 n
 y 
sin 1    
r 
  calc.  2 n
 y
tan 1    calc.  2 n
x
These rules give all values of the angles that could have a given trigonometric ratio. If
we want to deal with a reciprocal function, we just deal with the reciprocal of the ratio.
r
 x
For example, sec1    cos 1   . Therefore, if we wanted to take the sec1 1.797  ,
 x
r
 1 
we would just write cos 1 
 and then use the cosine inverse rule.
 1.797 
Find all values for each of the following in degrees. Round all answers at 3 decimal
places.
1) cos1  0.725 
7) cos1  0.152  
2) cot 1  2.715 
8) cot 1  12.172  
3) csc1  9.101 
9) csc1  3.472  
4) tan 1  2.500  
10) tan 1  0.505 
5) sin 1  0.707  
11) sin 1  0.789  
6) sec1  1.656  
12) sec1  3.816 
13) If (-7,-24) is a point on the
terminal side of angle A, find the
exact values of the following:
53
and is in
45
Quadrant III, find the following:
14) If sec B =
cos A =
sec A =
sin B =
csc B =
sin A =
csc A =
cos B =
sec B =
tan A =
cot A =
tan B =
cot B =
Find angle A rounded to three
decimal places (in degrees).
A = ____________________
Find angle B rounded to three
decimal
places (in radians).
B = ____________________
Use the unit circle that you filled out to find each of the following:
15) cos120
21) tan120
16) cos 210
22) tan 300
17) cos315
23) tan 225
18) sin120
24) sec120
19) sin135
25) csc120
20) sin 330
53
45
Note that you only have the cosine, sine, and tangent functions on your calculator. If we
want to know the value of a secant, cosecant, or cotangent, we just need to remember
their definitions. They are the reciprocal functions, so, for example, secant of 60° is
simply the reciprocal of the cosine of 60°. Reciprocal, recall, just means one over the
number, so if we wanted sec 60° from the calculator, we would simply enter 1/cos60° on
the calculator.
Use this information and your calculator to find the values of each of the following (note
that if there is no degree sign, your calculator should be in radians:
26) csc 47
29) csc13.45
27) sec 2.87
30) sec 245°
28) cot132
31) cot 2.33
32) Find the exact values of each of the following expressions. Use your unit circle to
find the values
 
 5 
a) cos    sin  
6
 6 
 7 
 3 
b) sec 
  tan  
 4 
 4 
33) Find the exact values of each of the following expressions. Use your unit circle to
find the values
a) sin  330   cos  30

b) 2csc  315  sec  225
