Right Triangle Trigonometry Trigonometry Basics Right Triangle Trigonometry

Sine Function When you talk about the sin of an angle, that means you are working with the opposite side, and the hypotenuse of a right triangle.

The Trigonometric Functions we will be looking at SINE COSINE TANGENT

The Trigonometric Functions SINE COSINE TANGENT

SINE Pronounced “sign”

COSINE Pronounced “co-sign”

Pronounced “tan-gent”

Represents an unknown angle Greek Letter q Prounounced “theta” Represents an unknown angle

Sine function Given a right triangle, and reference angle A: sin A = The sin function specifies these two sides of the triangle, and they must be arranged as shown. sin A = hypotenuse opposite A

Sine Function For example to evaluate sin 40°… Type-in 40 on your calculator (make sure the calculator is in degree mode), then press the sin key. It should show a result of 0.642787… Note: If this did not work on your calculator, try pressing the sin key first, then type-in 40. Press the = key to get the answer.

Finding sin, cos, and tan. (Just writing a ratio or decimal.)

Sine Function Sine Function Try each of these on your calculator:

Sine Function Sine Function Try each of these on your calculator:

Inverse Sine Function Inverse Sine Function Using sin-1 (inverse sin): If 0.7315 = sin θ then sin-1 (0.7315) = θ Solve for θ if sin θ = 0.2419

Cosine function Cosine Function The next trig function you need to know is the cosine function (cos): cos A = hypotenuse A adjacent

Cosine Function Cosine Function Use your calculator to determine cos 50° First, type-in 50… …then press the cos key. You should get an answer of 0.642787... Note: If this did not work on your calculator, try pressing the cos key first, then type-in 50. Press the = key to get the answer.

Cosine Function Cosine Function Try these on your calculator: cos 25°

Cosine Function Cosine Function Try these on your calculator:

Inverse Cosine Function Using cos-1 (inverse cosine): If 0.9272 = cos θ then cos-1 (0.9272) = θ Solve for θ if cos θ = 0.5150

Tangent function Tangent Function The last trig function you need to know is the tangent function (tan): tan A = opposite A adjacent

Tangent Function Use your calculator to determine tan 40° First, type-in 40… …then press the tan key. You should get an answer of 0.839... Note: If this did not work on your calculator, try pressing the tan key first, then type-in 40. Press the = key to get the answer.

Tangent Function Tangent Function Try these on your calculator: tan 5°

Tangent Function Tangent Function Try these on your calculator:

hypotenuse hypotenuse opposite opposite adjacent adjacent

10.8 9 A 6 Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

24.5 8.2 23.1 Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). 8.2 A 23.1 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

Finding a side. (Figuring out which ratio to use and getting to use a trig button.)

Ex: 1. Figure out which ratio to use. Find x Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x Shrink yourself down and stand where the angle is. tan 20 55 ) Now, figure out which trig ratio you have and set up the problem.

Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x tan 80  ( 72 ) ) = Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 3 Find the missing side. Round to the nearest tenth. Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x

Inverse Tangent Function Using tan-1 (inverse tangent): If 0.5543 = tan θ then tan-1 (0.5543) = θ Solve for θ if tan θ = 28.64

Finding an angle. (Figuring out which ratio to use and getting to use the 2nd button and one of the trig buttons.)

Ex. 1: Find . Round to four decimal places. tan 17.2 9 ) 17.2 9 Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem. Make sure you are in degree mode (not radians).

Ex. 2: Find . Round to three decimal places. 7 2nd cos 7 23 ) 23 Make sure you are in degree mode (not radians).

Ex. 3: Find . Round to three decimal places. 200 400 2nd sin 200 400 ) Make sure you are in degree mode (not radians).

Review Review These are the only trig functions you will be using in this course. You need to memorize each one. Use the memory device: SOH CAH TOA

Review The sin function: sin A = hypotenuse opposite A

Review Review The cosine function. cos A = hypotenuse A adjacent

Review Review The tangent function. tan A = opposite A adjacent

We need a way to remember all of these ratios…

When we are trying to find a side we use sin, cos, or tan. When we are trying to find an angle we use sin-1, cos-1, or tan-1.