8.4 Sine and Cosine Ratio
March 10, 2010
8.4: Sine and Cosine Ratio
SOH CAH TOA
(You'll find out what this means later.)
Objective: Use sine and cosine ratios to determine missing side lengths and angle measures in right triangles.
Feb 26­8:18 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
Warmup
Feb 26­8:29 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
Overview
• The tangent ratio involves both legs of a right
triangle.
• The sine and cosine ratio involve one leg and the hypotenuse of a right triangle.
Feb 26­8:37 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
The Sine Ratio
What is the sine of B?
Feb 26­8:43 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
The Cosine Ratio
What is the cosine of B?
Feb 26­8:50 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
Find the sine and cosine ratio of each angle.
sin(T) = sin(G) = cos(T) = cos(G) = Feb 27­11:38 AM
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8.4 Sine and Cosine Ratio
March 10, 2010
We can also use the sine and cosine ratio to find the side lengths of right triangles.
Ex) Find the value of x to the nearest 10th for each triangle.
x
x
53o
37o
Step 1: Which ratio, sine or cosine, are we going to use?
Step 2: Set up the ratio and solve for x.
Step 3: Use your calculator to solve for the side length.
Feb 27­12:00 PM
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8.4 Sine and Cosine Ratio
March 10, 2010
The Inverse of the Sine and Cosine Ratios
If we know the sine or cosine ratio, we can also use the inverse of these ratios to find a missing angle measure. opposite
o
sin­1( ) = x
hypotenuse
adjacent
o
cos­1( ) = x
hypotenuse
Step 1: Which ratio, sine or cosine, are we going to use?
Step 2: Set up the inverse ratio.
Step 3: Use your calculator to solve for the side length.
Feb 27­12:16 PM
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8.4 Sine and Cosine Ratio
March 10, 2010
How am I going to remember all this?
The key is:
SOH CAH TOA
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Memorize it, live it, love it.
Feb 27­1:50 PM
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8.4 Sine and Cosine Ratio
March 10, 2010
In summary...
• Sine, cosine, and tangent are ratios that relate the sides of a right triangle to each other.
• These ratios can be used to find missing angle measures and side lengths of right triangles. • The ratios can be used because, for a given angle, the sine, cosine
and tangent ratio will stay the same no matter the size of the triangle.
sin(x) = cos(x) = tan(x) = Feb 27­2:03 PM
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8.4 Sine and Cosine Ratio
March 10, 2010
Homework
Pg. 441
# 1 ­ 9 odd, 11 ­ 15 odd,
21, 22
Try for a challenge: # 31
Feb 27­2:59 PM
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