Lesson 2.8. There are 2 radians in a full rotation -- once around the circle There are 360° in a...
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Transcript of Lesson 2.8. There are 2 radians in a full rotation -- once around the circle There are 360° in a...
Lesson 2.8
There are 2 radians in a full rotation -- once around the circle
There are 360° in a full rotation To convert from degrees to radians
or radians to degrees, use the proportion
©Carolyn C. Wheater, 2000 3
degrees
360
radians
2
©Carolyn C. Wheater, 2000 4
Find the degree measure equivalent of radians.
degrees
360
radians
210
360
r
2
2360 420
420
360
7
6
r
r
degrees
360
radians
360
3 4
2
22 270
135
d
d
d
3
4
Find the radian measure equivalent of 210°
Reciprocal Identities
©Carolyn C. Wheater, 2000 5
sincsc
xx
1
cossec
xx
1
tancot
xx
1
tansin
cosx
x
x
cotcos
sinx
x
x
Quotient Identities
The angles whose terminal sides fall in quadrants II, III, and IV will have values of sine, cosine and other trig functions which are identical (except for sign) to the values of angles in quadrant I.
The acute angle which produces the same values is called the reference angle.
©Carolyn C. Wheater, 2000 8
Use the phrase “All Star Trig Class” to remember the signs of the trig functions in different quadrants.
©Carolyn C. Wheater, 2000 9
AllStar
Trig Class
All functions are positive
Sine is positive
Tan is positive
Cos is positive
Describe how to obtain the exact values of cos (π/4) and sin(π/4)
Reference angle: 45 so…
Sin (π/4) =
cos(π/4) =
Find the exact values of cos (5π/6) and sin(5π/6)
150 so Reference angle: 30, quadrant 3
Cos =
Sin = -1/2
Csc 300 - 1/sin =
Sec (11π/6)Ref. angle: 30, 1/cos =
Cot (3π/4) Ref angle: 45, -cos/sin = = -1
Exact: (cos 47.3, sin 47.3)
Hundredth: (.68, .73)
Pages 128 – 129
2-18 evens!