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```Right Triangle Trigonometry ­SOHCAHTOA and Pythagorean Thm
Before we begin: Read the "Why" section in your book on pg 220 AND put your calculator in "Degree" Mode
Define:
opposite side:
hypotenuse:
right triangle:
Given a right triangle and an acute angle θ, you can find the 6 trigonometric ratios.
SOH CAH TOA
A
hyp
opp
B
B
θ
C
csc θ
sin θ
sec θ
cos θ
cot θ
tan θ
cosecant, secant, and cotangent are reciprocal functions because their ratios are the reciprocals to sine, cosine, and tangent. This leads to the following relationships:
csc θ = 1 sec θ = 1 cot θ = 1 Additionally, from the definitions of sine, cosine, tangent, and cotangent functions, you can derive the following relationships too:
tanθ = _________
and cotθ = ________
1
Evaluate the exact values of the 6 trig functions of θ
EX a)
17
8
A
θ
15
Ex b)
20
θ
21
29
Ex c)
θ
13
5
12
Ex d) Given cos θ = 2/5 find the other five trig functions.
Ex e) If tan θ = 1/2 find the other 5 trig functions.
Ex f) If sin θ = 1/3 find the other 5 trig functions.
2
Inverse Trig functions can be used to find the measure of an acute angle:
(where θ = an angle measure)
If sin θ = x then θ = sin­1 x (because sinθ isn't sin times θ
you don't divide by sin!)
­1
If cos θ = x then
θ = cos x
­1
θm= tan x
If tan θ = x then Ex. Find the measure of θ. Round to the nearest
degree.
** Remember if mode isn't set for degree you'll have to do that first**
11
θ
26
12
θ
5
14
16
θ
a
15.7
12
θ = b
c
3
side 2 + side
One more right triangle tidbit: Pythagorean Thm a2 + b
= c2 = hyp
2
2
2
Use SOHCAHTOA AND Pythagorean Thm to solve the following missing measures.
Ex 1
Ex 2
b
θ
=c
5
8
17
a
θ
2
Ex. 4
Ex. 3
a
210
a
18
c
b
c
42
o
b
9
4
```
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