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TRIGONOMETRIC RATIOS - PowerPoint PPT Presentation

TRIGONOMETRIC RATIOS. goal: know how to set up different trig ratios. θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Don’t let it scare you… it’s like ‘x’ except for angle measure… it’s a way for us to keep our variables understandable and organized.

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TRIGONOMETRIC RATIOS

goal: know how to set up different trig ratios

θ this is the symbol for an unknown angle measure.

It’s name is ‘Theta’.

Don’t let it scare you… it’s like ‘x’ except for angle measure… it’s a way for us to keep our variables understandable and organized.

Where to start…

hypotenuse

opposite

opposite

Here are the ratios:

O

S

sinθ = opposite side

hypotenuse

H

A

C

hypotenuse

H

O

T

tanθ =opposite side

A

SOH CAH TOA

We could ask for the trig functions of the angleΘ by using the definitions.

c

b

SOHCAHTOA

SOHCAHTOA

Θ

INE

a

ANGENT

OSINE

PPOSITE

DJACENT

PPOSITE

DJACENT

YPOTENUSE

YPOTENUSE

So am I!

You need to pay attention to which angle you want the trig function of so you know which side is opposite that angle and which side is adjacent to it. The hypotenuse will always be the longest side and will always be opposite the right angle.

This method only applies if you have a right triangle and is only for the acute angles (angles less than 90°) in the triangle.

5

4

Θ

3

Let ∆ABC be a right triangle. The sine, the cosine, and the tangent of the acute angle A are defined as follows.

Trigonometric Ratios

b

cos A =

=

hypotenuse

c

Side opposite A

a

sin A =

=

hypotenuse

c

Side opposite A

a

tan A =

=

b

Write the ratio for sin L

Sin L= _a

c

Write the ratio for cosL

Cos L = _b_

c

Write the ratio for tan L

Tan L = _a_

b

M

c

a

N b L

Let’s switch angles: Find the sin, cos and tan for Angle M:

Tan M = _b_

a

Sin M = _b_

c

Cos M = _a_

c

Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given.

a

32

x

b

x

65

Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given.

d

c

x

56

opposite

sin S =

hypotenuse

cosS =

hypotenuse

opposite

tanS =

Ex. 2: Finding Trig Ratios—Find the sine, the cosine, and the tangent of the indicated angle.

opposite

sin S =

hypotenuse

cosS =

hypotenuse

opposite

tanS =

Ex. 1: Finding Trig Ratios the tangent of the indicated angle.

opposite

sin A =

hypotenuse

cosA =

hypotenuse

opposite

tanA =

Ex. 3: Finding Trig Ratios—Find the sine, the cosine, and the tangent of 45

opposite

sin 45=

hypotenuse

cos 45=

hypotenuse

opposite

tan 45=

√2

45

Ex. 4: Finding Trig Ratios—Find the sine, the cosine, and the tangent of 30

opposite

sin 30=

hypotenuse

cos 30=

hypotenuse

opposite

tan 30=