Trigonometry Chapter 9.1

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

Parts of a Right Triangle

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’.

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

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

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

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

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

The three trigonometric ratios θ 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

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.

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.

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.