Original Power PointFrom

mackinac.eup.k12.mi.us/cms/lib/Mackinac Island Public School

Author:Mrs. Bennett

The Trigonometric Functions we will be

looking at

SINE

COSINE

TANGENT

Old Hippie

Old Hippie

SomeOldHippieCameAHoppin’ThroughOurApartment

SOHCAHTOA

Old Hippie

Old Hippie

SinOppHypCosAdjHypTanOppAdj

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.

5520 m

x

20

55tanx

m 6.28x

x55tan20tan 20 55 )

Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

Ex: 2 Find the missing side. Round to the nearest tenth.

72

80 ft

x

x

8072tan

ft 26x

8072tan x

72tan

80x

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.

New Version…

The Trigonometric Ratios

SINECOSINETANGENT

The trigonometric ratios can be used to find a missing side of a right triangle or an

angle.

I smell a hippie!

SOH CAH TOA

Old Hippie

Old Hippie

SinOppHypCosAdjHypTanOppAdj

Some

Old

Hippie

Came

AHoppin’

Through

OurApartment

Maybe this will help…

Old Hippie

Old Hippie

I knew I smelled a hippie!!

Now, how do we use this trig stuff?

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Label the sides of the triangle using the reference angle as the starting point.

Draw an arrow straight from the reference angle, that is the opposite Leg

Opposite Leg

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Opposite the right angle is the hypotenuse.

Opposite Leg

Hypotenuse

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Lastly, label the remaining leg the Adjacent Leg

Opposite Leg

Hypotenuse

Adjacent Leg

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

The triangle gives you the ADJACENT LEG and is looking for the OPPOSITE LEG.

Opposite Leg

Hypotenuse

Adjacent Leg

Step 1Figure out which ratio to use.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

TANGENT uses the OPPOSITE and ADJACENT leg

Opposite Leg

Hypotenuse

Adjacent Leg

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Plug in the information present.

Opposite Leg

Hypotenuse

Adjacent Leg

Tan(55)=

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Insert a “1” under the Tan(55).

Opposite Leg

Hypotenuse

Adjacent Leg

=

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Cross multiply

Opposite Leg

Hypotenuse

Adjacent Leg

=

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Cross multiply

Opposite Leg

Hypotenuse

Adjacent Leg

20 ∙𝑇𝑎𝑛 (55 )=𝑥

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Enter that into your calculator..

20 ∙𝑇𝑎𝑛 (55 )=𝑥

Adjacent Leg

Opposite Leg

Hypotenuse

Step 2Using the Trig ratio.

5520 m

x

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

The calculator does all of the hard work!

2 8.56=𝑥

Step 2Using the Trig ratio.

5520 m

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

That is your answer.

28.56 m

Step 2Using the Trig ratio.

5520 m

𝑆𝑜h𝐶𝑎h𝑇𝑜𝑎

Done!

28.56 m

They all work the same man! It works every time!!