1. Right Triangle Trigonometry
hypotenuse
hypotenuse
opposite
adjacent
adjacent
opposite
reciprocal functions
*** “SOH CAH TOA” ***

2. Right Triangle Trigonometry, cont.
Find the six trig functions for the given triangle.
1. Find the missing side measurement:
Recall the Pythagorean Theorem:
c2 = a2 + b2
hyp
side
side 5
c2 = 4
c2 =
c2 = 25
c = 5
hyp 3
2. Find the six trig functions
“SOH CAH TOA”
opp
hyp

3. Common Pythagorean Triples (CPT’s)
**memorize!!!**
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
& multiples
6, 8, 10
10, 24, 26
16, 30, 34
14, 48, 50
9, 12, 15
etc.

4. Special Right Triangles
45o – 45o – 90o
30o – 60o – 90o
45o
30o 2 1
45o
60o 1 1
**memorize**
ex. sin 60o =
NOTICE:
sin 60o =
ex. cos 45o =
ex. tan 30o =

5. csc und. sec 1 und. cot und. 1 2 3 4 4 3 2 1 degrees radians undefined1 2 3 4
(y) 4 3 2 1
(x)
undefined
csc
und.
recip-rocals of above
sec 1
und.
cot
und.

6. Cofunctions not the same as reciprocal functions
NOTICE: sin 30o = = cos 60o (because 30o and 60o are complementary angles)
In general cofunctions of complementary angles are equal.
Ex. sin 40o = cos 50o
cot 35o = tan 55o etc.

7. Fundamental Trigonometric Identities
**memorize**
Reciprocal Identities:
Quotient Identities:
Pythagorean Identities:
y x = 1
(unit circle)
leg leg = 1

8. How to remember Pythagorean Identities
clue: pythagorean
*memorize this one 3
Then, by alg:
Also: 3
And:
Also: 3
And:
3 groups of 3: 9 total

9. Examples find the values of cos and tan .62 + x2 = 1 .36 + x2 = 1
y x = 1
x2 = 1 .6
opp.
x2 = 1
(sin) (y)
x2 = .64
x = .8
now know all 3 parts of
so cos = .8
And tan

10. Examples, cont.
Use trigonometric identities to transform one side of the equation to the other.
**work on ONE side ONLY**
Do NOT operate across the = sign

11. Examples, cont. Solve: tan 71.5 = 50 tan 71.5 = x 400 yd x 71.5o
hyp. x
opp.
71.5o
200 yd.
opp.
50 ft.
adj.
So use sin:
So use tan:
tan 71.5 =
*When looking for an angle use inverse trig function
i.e. where does sin theta = 1/2
50 tan 71.5 = x

12. Examples, cont. Find the value of in degrees and radians. Evaluate:
tan 33.5o
*When looking for an angle use inverse trig function
radians: