Transcript 14.3 Converting Between Degrees and Radians and Inverse

14.3 Converting Between Degrees
and Radians and
Inverse Trigonometry
Converting Between
Degrees and Radians

When we convert between degrees and
radians we multiply by a
.
1

The easiest value that is equivalent is
180º
radians and
degrees.

So, to convert from degrees to radians we

multiply by
.
180
And to convert from radians to degrees we
multiply by 180 .


π
Convert each angle measure from
degrees to radians.
1.
  120
2.
  30
3.
  410
o
o
o
Convert each angle measure from
radians to degrees. Round to the
nearest tenth.
4.   7
6
5.


3
6.
5

2
Revolutions Greater than a Full
Circle
The unit circle continues to revolve past a full circle in both
the positive and the negative direction.
angle
 An
is determined by rotating a ray about
its vertex.
side
initial
 The
of an angle is
the ray extending from the vertex before rotation.
 The resulting ray, after the rotation, is called the
terminal
side
.

When the initial side coincides with the positive x-axis and
the vertex is at the origin, it is said to be in

.
standard
position


In order to evaluate trig functions of
angles larger than one revolution, it is
helpful to determine where on the unit
circle the value lies by working backwards.

To find that value, you can subtract a full
circle until you get a value that is on the
first revolution.
Sketch the angle in standard form
and evaluate the trig function.
7. cos 495
o
8. sin 570
o

Sketch the angle in standard form
and evaluate the trig function.
 19 
9. cos  

6 
9
10. sin
4

Sometimes you will be given the value of
the trigonometric function and you will
need to work backwards to find the point
on the unit circle that corresponds to
that value.

Typically you will be looking at one
revolution of the unit circle – so between
0 and in radians and between 0° and
360° in degrees.
Find θ such that 0  
 2 .
3
11. sin  
2
3
2

Is
positive or negative?

In which quadrant(s) is the sin value
positive?

What real number, θ , has a y-coordinate
of 3 ?
2
Find θ such that 0  

1
sec
 2
12.

 2 .

Positive or negative?

What quadrant(s) is secant negative in?

What is the reciprocal of  2 ?

What real number, , has an x-coordinate
of  2 ?
2
Find θ such that 0    360 .
o
13.
o
 3
arc tan 

 3 

Positive or negative?

What quadrant(s) is tangent positive in?

Where is tangent equal to
3 ?
3
Find θ such that 0    360 .
o
14. csc   undefined

Positive or negative?

What does this mean about sin?

Where is sinθ = 0?
o

Use the unit circle below to help
remember when each trig function is
positive.
Find θ such that 0  
15. cot    3
2 3
17. csc   
3
 2 .
1
16. sin  2 
 
1
18.
 2
arc cos 

 2 
Find θ such that 0    360 .
o

3
19. sin   
 2 
1
21.
sin  0
o
3
20. cos  
2
22. cot
1
1
Evaluate.
23. sin
1
 cos180 
5 

25. sin  cos 
3 

1
5 

24. cos  cos 
4 

1
26. tan 1  tan135
