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Section 92 Sine and Cosine Ratios SPI 32F: determine the trigonometric ratio for a right triangle ne

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... we looked at a tangent trigonometric function. Now we will investigate: ... Sine and Cosine: involves one leg and the hypotenuse. Writing Sine and Cosine Ratios ... – PowerPoint PPT presentation

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Title: Section 92 Sine and Cosine Ratios SPI 32F: determine the trigonometric ratio for a right triangle ne


1
Section 9-2 Sine and Cosine
Ratios SPI 32F
determine the trigonometric ratio for a right
triangle needed to solve a real-world problem
given a diagram
  • Objectives
  • Use sine and cosine ratios to determine side
    lengths in triangles
  • Previously, we looked at a tangent trigonometric
    function. Now we will investigate
  • sine
  • cosine

Remember, they only apply to right triangles!
2
Trigonometry and the Tangent Ratio
Tangent Ratio In a right triangle, the ratio of
the length of the leg opposite ?P to the length
of the leg adjacent to ?P is constant, no matter
what lengths are chosen for the sides. This is
called the tangent ratio.
Tangent of ?P opposite leg
adjacent leg
3
Sine and Cosine Ratio
Tangent Ratio involves both legs of a right
triangle Sine and Cosine involves one leg and
the hypotenuse
Sine (sin P) of ?P opposite leg
hypotenuse
Cosine (cos P) of ?P adjacent leg
hypotenuse
4
Writing Sine and Cosine Ratios
Use the triangle to write each ratio.
opp hyp
8 17
a. Sin T

adj hyp
15 17
b. Cos T

opp hyp
15 17
c. Sin G

adj hyp
8 17
d. Cos G

5
Inverse of Sin and Cos
Use the Inverse function to find the measures of
an angle.
Find the m?L to the nearest degree.
Method 1. (cos -1)
cos L 2.5 4.0 m ?L cos-1
(2.5/4) 51.3 m?L ? 51
Method 2. (sin -1)
sin L 3.1 4.0 m ?L sin-1
(3.1/4.0) 50.8 m ?L ? 51
6
Real-world Connection
A 20-ft. wire supporting a flagpole forms a 35
angle with the flagpole. To the nearest foot, how
high is the flagpole?
The flagpole, wire, and ground form a right
triangle with the wire as the hypotenuse.
Because you know an angle and the measures of its
adjacent side and the hypotenuse, you can use the
cosine ratio to find the height of the flagpole.
The flagpole is about 16 ft tall.
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