SOHCAHTOA

Write down everything you know about triangles.

Include any vocabulary related to triangles that you may have learned.

Include Diagrams.

Be Creative….

I like the Nick Name

RATS!

Imagine the pitcher stands at the pitcher’s mound at one of the acute angles. S/he throws the ball to the side which is opposite to him/her.

Pitcher’s Mound

opposite

From the opposite side, the player throws the ball to the player at the hypotenuse.

11Pitcher’s Mound

opposite 2233 hypoteneuse

The player at the hypotenuse throws the ball to the last side of the triangle which is the adjacent.

11Pitcher’s Mound

Opposite 2233 Hypoteneuse

44 Adjacent

Every right angled triangle has three sides labelled from a reference angle.

HypoteneuseHypoteneuse

OppositeOpposite

AdjacentAdjacent

Reference Angle

What happens if we move the reference angle?

Discuss this with a partner? How does this change the labels on the sides?

Reference Angle

The adjacent and the opposite are switched!

The Hypotenuse stays the same!

Reference Angle

Adjacent

Hypotenuse—doesn’t change!

Opposite

Label all the three sides from the reference angle.

HH

A

A

O

O

AA

€

sinΘ =opposite

hypoteneuse=O

H

€

cosΘ =adjacent

hypoteneuse=A

H

€

tanΘ =opposite

adjacent=O

A

€

sin ANGLE NAME =length of opposite

length of hypoteneuse

€

cos ANGLE NAME =length of adjacent

length of hypoteneuse

€

tan ANGLE NAME =length of opposite

length of adjacent

Here is a quick way to remember the sides that correspond to each ratio.

€

S O H C AH T O A

S O H C A H T O A

Have you noticed three buttons on your calculator?

SinSin CosCos TanTan

These buttons relate to the three trig ratios we have shown from the RATS.

The calculator can calculate the ratio for any given angle instantly.

SinSin CosCos TanTan

Find the sin 98 °.

You may need to determine if you press the sin button or enter 98 first.

Try this on your calculator: Answer is: 0.990268068

Check to see if your calculator is in the wrong mode.

✔ Right Mode: Degree, D, Deg

✗ Wrong Modes: Grad, Rad

Find your Mode Button to change it to Degrees and try the question again.

ModeMode

SinSin CosCos TanTan

Find the following ratios using your calculator to 4 decimals:

sin 45°=

cos 60°=

tan 57°=

0.7071

0.5

1.5398

Sin-1Sin-1 Cos-1Cos-1 Tan-1Tan-1

Find the above buttons on your calculator.

They may be above your sin/cos/tan keys.

You may need to use a Second Function Key or another key to access these additional functions on your calculator.

These buttons help you find the angle if you are given the trig ratio. I call this ‘going backwards’.

Sin-1Sin-1 Cos-1Cos-1 Tan-1Tan-1

Let’s try the following example.

Find the angle if:

€

sin B =4

5€

Method 1: Enter 4 ⁄ 5 on your calculator and enter second function sin

Method 2: Enter second function sin ( 4 ⁄ 5) on your calculator

ANSWER: 53.13 degrees

What are the three trig ratios from the reference angle.

5

4

3

€

sinθ =3

5

€

tanθ =3

4€

cosθ =4

5

Find the three ratios from the following triangle.

8

1214

✔✔

€

sinθ =8

14

€

tanθ =8

12=

2

3€

cosθ =12

14

√

7 15

✔A✔A

€

sinA =7

15

S O H C A H T O A

Starting at the reference angle decide which two sides you have. Pick the trig ratio that uses those two sides.

O H

Ask yourself: What sides do I have? Which Trig Ratio uses those two sides!

6

25

✔B✔B

€

tanB =6

25

36

25

✔C✔C

€

cos C =25

36

Ask yourself: What sides do I have?Which Trig Ratio uses those to sides!

Find the missing side x.

56°

20X

Have: Hypoteneuse Need: Adjacent

Use the Cosine Ratio

56°

20X

56°

20X

€

cos 56 =x

20

56°

20X

€

cos 56 =x

20x = cos 56 × 20

x = 11.18

Find the missing side x.

35°

x12

What is the side you have and what is the side you need?

Have: OppositeNeed: Hypotenuse

Use the Sine Ratio

35°

x12

The ratio that uses both the O and the H is the sin ratio.

35°

X is the hypotenuse12 is the opposite side

Now we can fill in the ratio:

35°

X 12

€

sin 35 =12

x

Now we can fill in the ratio:

€

sin 35 =12

xSolve for x in the above equation by using the ‘Switcheroo’

€

x =12

sin35= 20.92

If the side you are missing is in the NUMERATOR such as:

€

sin43 =x

12Then multiply the two values together x=sin 43 x 12

If the side you are missing is in the DENOMINATOR such as:

€

cos43 =7

xThen use the ‘switcheroo’ to switch the cos 43 and the x

Answer would be 7÷(cos 43)

Case 1: Multiply ×

Case 2: Switcheroo ÷

I hope this was everything you needed to know about trigonometry!