a. sin17 b. cos 73 c. sin 65 d. cos 25 sin(a) = cos (90 a) properties of... ·...
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AdvAlg103PropertiesOfTrigonometricRatios.notebook
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a. sin17o b. cos 73o c. sin 65o d. cos 25o
sin(A) = cos (90 A)
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Find another pair of angle measures x and y that illustrates the pattern cos x = sin y.
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If two angles are complementary(add to 90o), the sine of one angle equals the cosine of the other.
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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
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AND
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from previous page
from previous page
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shorter leg is half the hypothenuse
60o
30o
1
45o
45o1
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Complements Thm.
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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
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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.
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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?
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cos 600 = ½cos 450 = √2 2cos 300 = √3 2
cos = sin (90 - ) and thesin = cos ( 90 - )
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(cos )2 + ( sin )2 = 1 or( sin )2 + ( cos )2 = 1
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Use the triangles and the lengths of each leg to complete the table below.
tan = sin cos
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Practice:
1. Sin 49º = ______________ Cos 27º = ______________
2. Cos θ = .187 Find the Sin θ =
3. Cos θ = .956 Sin θ = .292 Find Tan θ
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A
BC30 o
18
Find the exact value of AC and BC.
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5EF
G
Find the exact values of EG and FG.
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Suppose sin θ =
What is the value of cos θ ?
What is the value of tan θ ?
√ 65
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Suppose cos θ = and tan θ = 3,
what is the value of sin θ ?
√ 1010
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tan(x) = 1/6
tan1(tan(x)) = tan1(1/6)
x= tan1(1/6) 9.462o
x
x
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