Upload
others
View
65
Download
0
Embed Size (px)
Citation preview
AdvAlg103PropertiesOfTrigonometricRatios.notebook
1
May 03, 2018
Mar 910:08 PM
a. sin17o b. cos 73o c. sin 65o d. cos 25o
sin(A) = cos (90 A)
AdvAlg103PropertiesOfTrigonometricRatios.notebook
2
May 03, 2018
Mar 910:11 PM
Find another pair of angle measures x and y that illustrates the pattern cos x = sin y.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
3
May 03, 2018
Mar 910:12 PM
If two angles are complementary(add to 90o), the sine of one angle equals the cosine of the other.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
6
May 03, 2018
Mar 910:27 PM
The Pythagorean Identity can be used to find the value of the sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle.
Not interested in finding the angle measure just the sine of the angle or the cosine of the angle
AdvAlg103PropertiesOfTrigonometricRatios.notebook
8
May 03, 2018
Mar 910:33 PM
from previous page
from previous page
AdvAlg103PropertiesOfTrigonometricRatios.notebook
9
May 03, 2018
Mar 910:36 PM
shorter leg is half the hypothenuse
60o
30o
1
45o
45o1
AdvAlg103PropertiesOfTrigonometricRatios.notebook
16
May 03, 2018
Mar 911:00 PM
The cosine function gets its name from the fact that the cosine of an angle is equal to the sine of the complement of the angle. In addition, the sine of an angle is equal to the cosine of the complement of the angle.
Even though the tangent function has been defined as opposite leg over adjacent leg of a right triangle, it is also define as the ratio of the sine of an angle divided by the cosine of the same angle.
We should know the exact value of sine, cosine, and tangent for 30o, 45o, and 60o angles.
The Pythagorean Identity can be used to find the value of sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
17
May 03, 2018
Mar 911:00 PM
The cosine function gets its name from the fact that the cosine of an angle is equal to the sine of the complement of the angle. In addition, the sine of an angle is equal to the cosine of the complement of the angle.
Even though the tangent function has been defined as opposite leg over adjacent leg of a right triangle, it is also define as the ratio of the sine of an angle divided by the cosine of the same angle.
We should know the exact value of sine, cosine, and tangent for 30o, 45o, and 60o angles.
The Pythagorean Identity can be used to find the value of sine of an angle if we are given the cosine of the angle or to find the cosine of an angle if we are given the sine of the angle.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
18
May 03, 2018
Dec 273:58 PM
Notes 10-3Find the length of each leg. Use exact values, no decimals.
Use the triangle to complete thetable. Use exact values, no decimals.
What similarities do you see in the table?
AdvAlg103PropertiesOfTrigonometricRatios.notebook
19
May 03, 2018
Dec 274:04 PM
cos 600 = ½cos 450 = √2 2cos 300 = √3 2
cos = sin (90 - ) and thesin = cos ( 90 - )
AdvAlg103PropertiesOfTrigonometricRatios.notebook
20
May 03, 2018
Dec 274:19 PM
(cos )2 + ( sin )2 = 1 or( sin )2 + ( cos )2 = 1
AdvAlg103PropertiesOfTrigonometricRatios.notebook
21
May 03, 2018
Dec 274:20 PM
Use the triangles and the lengths of each leg to complete the table below.
tan = sin cos
AdvAlg103PropertiesOfTrigonometricRatios.notebook
22
May 03, 2018
Dec 274:21 PM
Practice:
1. Sin 49º = ______________ Cos 27º = ______________
2. Cos θ = .187 Find the Sin θ =
3. Cos θ = .956 Sin θ = .292 Find Tan θ
AdvAlg103PropertiesOfTrigonometricRatios.notebook
23
May 03, 2018
Sep 298:49 AM
A
BC30 o
18
Find the exact value of AC and BC.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
24
May 03, 2018
Sep 298:52 AM
5EF
G
Find the exact values of EG and FG.
AdvAlg103PropertiesOfTrigonometricRatios.notebook
25
May 03, 2018
Sep 298:58 AM
Suppose sin θ =
What is the value of cos θ ?
What is the value of tan θ ?
√ 65
AdvAlg103PropertiesOfTrigonometricRatios.notebook
26
May 03, 2018
Sep 299:02 AM
Suppose cos θ = and tan θ = 3,
what is the value of sin θ ?
√ 1010
AdvAlg103PropertiesOfTrigonometricRatios.notebook
43
May 03, 2018
Mar 911:12 PM
tan(x) = 1/6
tan1(tan(x)) = tan1(1/6)
x= tan1(1/6) 9.462o
x
x