Trigonometry

Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles

What is the acronym we use to remember trig functions?

SOH CAH TOA

Sin θ

Sin θ = 5/13

Tan θ=6/8=3/4

Write the ratio you would use to find x

Cos θ = x / 11

What ratio would you create given the information?

Cos θ = 4 / 5

Find x

Tan 32 = x / 13 X = 8.1°

Find x

Cos 37 = 11 / x X = 13.7

Find θ

Cos -1 ( 4.4/11) θ = 66.4°

Find θ

Tan -1 ( 7.7 / 14) θ = = 28.8°

Find all the missing parts of the triangle

What is the law of sines?

Sin A = Sin B = Sin C a b c

Set up the ratio for AB in the following triangle

Sin 53 = Sin 44 X 7

Solve for angle b

Sin b = Sin B = 6.8°

Find BC

Sin 29 = Sin X X = 33

Draw the triangle. Solve for the missing pieces m ∠ C = 145° b = 7 c = 33

m ∠ A = 28° m ∠ B = 7° a = 27

What is the traditional law of cosines?

Set up the formula to find BC

x 2 = – 2(30)(21)cos123

Solve for AB

AB = 21

Find the measure of angle A

A = 137°

Solve the triangle

What are the two special right triangles?

30 – 60 – – 45 – 90

What is the relationship between the side lengths in a 45 – triangle?

The legs are the same The hypotenuse is Leg√2

What is the relationship between the side lengths of a 30 – 60 – 90 triangle?

Long leg = SL√3 Hypotenuse = 2 * SL

Solve for x and y