1. Trigonometry
Chapter 9.1

2. Trigonometry Trigonometry is the study of triangle measurement
A trigonometric ratio is a ratio of the lengths of two sides of a right triangles.

3. Parts of a Right Triangle

4. The sine ratio the length of the opposite side The ratio of
the length of the hypotenuse
The ratio of
is the sine ratio.
In trigonometry we use the Greek letter θ, theta, for the angle. The value of the sine ratio depends on the size of the angles in the triangle. θ O P S I T E H Y N U
We say:
sin θ =
opposite
hypotenuse
The sine ratio depends on the size of the opposite angle. We say that the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse.
Sin is mathematical shorthand for sine. It is still pronounced as ‘sine’.

5. Example 1 A. Express sin L as a fraction
Find Sine, Cosine, and Tangent Ratios
A. Express sin L as a fraction

6. The cosine ratio the length of the adjacent side
the length of the hypotenuse
The ratio of
is the cosine ratio.
The value of the cosine ratio depends on the size of the angles in the triangle. θ
We say,
cos θ =
adjacent
hypotenuse
A D J A C E N T H Y P O T E N U S

7. Example 1 A. Express cos L as a fraction
Find Sine, Cosine, and Tangent Ratios
A. Express cos L as a fraction

8. The tangent ratio the length of the opposite side
the length of the adjacent side
The ratio of
is the tangent ratio.
The value of the tangent ratio depends on the size of the angles in the triangle. θ O P S I T E
We say,
tan θ =
opposite
adjacent
A D J A C E N T

9. Example 1 A. Express tan L as a fraction
Find Sine, Cosine, and Tangent Ratios
A. Express tan L as a fraction

10. The three trigonometric ratiosθ O P S I T E H Y N U
A D J A C E N T
Sin θ =
Opposite
Hypotenuse
S O H
Cos θ =
Adjacent
Hypotenuse
C A H
Tan θ =
Opposite
Adjacent
T O A
Stress to students that they must learn these three trigonometric ratios.
Students can remember these using SOHCAHTOA or they may wish to make up their own mnemonics using these letters.
Remember:
S O H
C A H
T O A

11. Find a missing side length
In triangle ABC, where AB is the hypotenuse, AB= 10 and the m<B=40°, find the length of side AC.

12. Find a missing side length
In triangle XYZ, where XY is the hypotenuse, YZ= 15 and the m<Y=35°, find the length of side XZ.

13. Find a missing side length
In triangle ABC, where AB is the hypotenuse, AB= 16 and the m<A=35°, find the length of side BC.
In triangle ABC, where AB is the hypotenuse, AB= 24 and the m<B=18°, find the length of side BC.
In triangle ABC, where AB is the hypotenuse, BC= 16 and the m<A=35°, find the length of side AC.
In triangle ABC, where AB is the hypotenuse, AC= 32 and the m<A=64°, find the length of side BC.