Download Chief SOHCAHTOA

Chief SOHCAHTOA
Objective: I will be able to:
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Define the three basic trig ratios and their reciprocal functions.
Given two sides of a right triangle, find the third side and write all 6 trig ratios in simplest
form.
Given two trig ratios for a triangle, find the third side and write all 6 trig ratios in simplest
form.
Given one trig ratio for a triangle, find the third side and write all 6 trig ratios in simplest form.
FINDING A MISSING SIDE OF A TRIANGLE--Review
When working with right triangles, it is often necessary to use the Pythagorean Theorem.
Remember, if you are given ANY two sides, then the Pythagorean Theorem will allow you to find the
missing side.
2
2
a2+b2=c2 ----- In other words  leg1    leg 2   hyp 2 .
THREE BASIC TRIG RATIOS--Definitions
The three basic trig ratios can be used for ANY right triangle. You may use Chief SohCahToa’s name
to help you remember them. In trigonometry, we frequently use the Greek letters theta,  , and alpha,
 , to represent angles.
The three ratios are sine, cosine, and tangent. We use their abbreviations sin, cos, and tan. However,
these abbreviations are ALWAYS followed by an angle name or measure. Never just write sin, cos, or
tan.
opp
sin  
Hypotenuse
hyp
Opp—This is the
adj
side opposite to the
cos  
hyp
angle  .
opp
tan  

adj
Adj--- This is the side
ADJACENT to the
angle 
RECIPROCAL TRIG RATIOS
In addition to the three basic trig ratios, there are three RECIPROCAL ratios. These reciprocal ratios
are cosecant, secant, and cotangent. We use their abbreviations csc, sec, and cot. However, these
abbreviations are ALWAYS followed by an angle name or measure.
The reciprocal of sine is cosecant.
The reciprocal of cosine is secant.
The reciprocal of tangent is cotangent.
opp
hyp
sin  
csc  
hyp
opp
adj
hyp
cos  
sec  
hyp
adj
opp
adj
tan  
cot  
adj
opp
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NOTE: The two words that begin with “co”
never together!
Given 2 sides of a right triangle, find the 3rd side & write all 6 trig ratios in simplest form.
Given:
2
1

Step 1: Label the triangle.
2 hyp
1
opp

Step 2: Find the missing side by using Pythagorean Theorem.
adj2 + opp2 = hyp2
1
adj2 + 12= 22
opp
2
adj = 3
adj

adj = 3
adj =
Step 3: Write the three basic ratios.
1
sin  
2
3
cos  
2
1
3
tan  
which equals tan  
3
3
2 hyp
3
Step 4 Write the three reciprocal ratios.
2
csc  
1
2
2 3
sec  
which equals sec  
3
3
cot  
3
1

Given two trig ratios for a triangle, find the third side and write all 6 trig ratios in simplest
form.
2
5
cos  
Given sin  
3
3
Step 2: Check to see if it labeled correctly by
Step 1: Label the triangle.
using Pythagorean Theorem.
hyp=3
adj2 + opp2 = hyp2
opp=2
22 + 5 2= 32

4+5= 9
adj= 5
Step 4 Write the three reciprocal ratios.
3
csc  
2
3
3 5
sec  
which equals sec  
5
5
Step 3: Write the three basic ratios.
2
sin  
3
5
cos  
3
tan  

2
5
which equals tan  
2 5
5
cot  
5
2
Given one trig ratio for a triangle, find the third side and write all 6 trig ratios in simplest
form.
hyp
Given: sec  3 Remember sec  
adj
Step 2: Find the missing side by using Pythagorean Theorem.
Step 1: Label the triangle.
adj2 + opp2 = hyp2
hyp=3
hyp=3
opp
12 + opp2= 32

adj=1
Step 3: Write the three basic ratios.
2 2
sin  
3
1
cos  
3
2 2
tan  
1
opp2= 8
opp =
8 =2 2
opp = 2 2
Step 4 Write the three reciprocal ratios.
3
3 2
csc  
which equals
4
2 2
3
sec  
1
1
2
cot  
which equals
4
2 2

adj=1