quiz 1) fill in the sides lengths for the following triangle (and label them hyp, opp, adj): 30º 2)...
TRANSCRIPT
Quiz
1) Fill in the sides lengths for the following triangle (and label them hyp, opp, adj):
30º2) Find the compliment, supplement, and 2 coterminal angles for an angle that is 62.5º
1
2
3
OPP
HYP
ADJ
Compliment – 27.5, supplement – 117.5, coterminals 422.5 and -297.5
You can also measure angles in radians.
One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length r.
Since the circumference of a circle is 2πr, there are 2π radians in a full circle.
Degree measure and radian measure are therefore related by the following:
360º = 2π radians
r r
one radian
Conversion Between Degrees and Radians
Use the Proportion:
360 2
x radians
You plug in either the degree or radians that you are given and cross multiply to get the answer
Examples: Change each in radiansa. 240º b. 135º
360 2
x radians
360 2
x radians
240
360 2
r
240(2 ) 360r 480 360r 360 360
4
3r
135(2 ) 360r 270 360r 360 360
3
4r
135
360 2
r
Examples: Change each in radiansa. 240º b. 135º
4
3r
3
4r
What does this mean?
It means that in the first case 240º is equal to radians4
3
And in the 2nd case 135º is equal to
radians
3
4
Examples: Rewrite each in degreesa. 5π 8
360 2
x radians
58
360 2
x
5(2 ) 360
8x
2 1800
1 8
x
1800 16 x 1616
112.5 x
Be careful with the multiplications
Examples: Rewrite each in degreesa. 2π 3
360 2
x radians
23
360 2
x
2(2 ) 360
3x
2 720
1 3
x
720 6 x 66
120 x
The most common conversions
306radians
454radians
603radians
902radians
180radians
2 360radians
We will add several more to this chart next class so leave some room