Transcript Trigonometry - Blog 44 Sites

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.
opposite
Pitcher’s
Mound

From the opposite side, the player throws the
ball to the player at the hypotenuse.
opposite
2
3
hypoteneuse
1
Pitcher’s
Mound

The player at the hypotenuse throws the ball
to the last side of the triangle which is the
adjacent.
Opposite
3
2
Hypoteneuse
1
4
Adjacent
Pitcher’s
Mound

Every right angled triangle has three sides
labelled from a reference angle.
Hypoteneuse
Opposite
Reference
Angle
Adjacent


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
Hypotenuse—doesn’t
change!
Adjacent
Opposite

Label all the three sides from the reference
angle.
A
H
H
O
A
O
A
A
opposite
O
sin  

hypoteneuse H
adjacent
A
cos 

hypoteneuse H
opposite O
tan  

adjacent A
length of opposite
sin ANGLE NAME 
length of hypoteneuse

length of adjacent
cos ANGLE NAME 
length of hypoteneuse

length of opposite
tan ANGLE NAME 
length of adjacent

Here is a quick way to remember the sides that
correspond to each ratio.
SOHCAHTOA
S
O
H
CAH T
O
A

Have you noticed three buttons on your
calculator?
Sin
Cos
Tan
These buttons relate to the three trig ratios
we have shown from the RATS.
Sin

Cos
Tan
The calculator can calculate the ratio for any
given angle instantly.
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.
Mode

✔ Right Mode: Degree, D, Deg

✗ Wrong Modes: Grad, Rad

Find your Mode Button to change it to
Degrees and try the question again.
Sin
Cos
Tan
Find the following ratios using your calculator to 4
decimals:
sin 45°= 0.7071
cos 60°= 0.5
tan 57°= 1.5398
Sin-1
Cos-1
Tan-1
These buttons help you find the angle if you are
given the trig ratio. I call this ‘going backwards’.
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.
Sin-1
Cos-1
Tan-1
Let’s try the following example.
Find the angle if:
4
sin B 
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
3
4
3
sin  
5
3
tan  
4

4
cos  
5

Find the three ratios from the following
triangle.
✔
14
12
8
8
sin  
14
12
cos  
14
8 2
tan  

12
3


√
SOHCAHTOA
Starting at the reference angle decide which two sides
you have. Pick the trig ratio that uses those two sides.
7
O
15
7
sin A 
15
H
✔
A


Ask yourself: What sides do I have?
Which Trig Ratio uses those two sides!
6
tanB 
25
6
25
✔
B


Ask yourself: What sides do I have?
Which Trig Ratio uses those to sides!
25
cos C 
36
36
25
✔
C


56
°
Find the missing side x.
20
X



56
°
Have: Hypoteneuse
Need: Adjacent
Use the Cosine Ratio
20
X
x
cos 56 
20
56
°
20
X
x
cos 56 
20
x  cos 56  20
x  11.18
56
°
20
X

Find the missing side x.
x
12
35
°
What is the side you have and what is the
side you need?
Have: Opposite
Need: Hypotenuse
Use the Sine Ratio
x
12
35
°

The ratio that uses both the O and the H is
the sin ratio.
12 is the opposite
side
X is the hypotenuse
35
°

Now we can fill in the ratio:
12
sin 35 
x
12
X
35
°

Now we can fill in the ratio:
12
sin 35 
x
12
x
 20.92
sin 35
Solve for x in the
above equation by
using the
‘Switcheroo’

If the side you are missing is in the
NUMERATOR such as:
x
sin 43 
12
Then multiply the two values together
x=sin 43 x 12


If the side you are missing is in the
DENOMINATOR such as:
7
cos 43 
x
Then 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!