1. The Trigonometric Functions and Right Triangles
A P o w e r P o I n t L e s s o n
By Michael V. Schuster Mathematics Faculty Our Lady of the Sacred Heart High School Coraopolis, Pennsylvania

2. Right Triangle Anatomy
Hypotenuse
Opposite 
Adjacent

3. Right Triangle Anatomy
Hypotenuse
Adjacent
Opposite

4.  Trigonometric Functions as Ratios of Sides OPP SIN q HYP ADJ COS q=
HYP
ADJ
COS q =
HYP
HYP
OPP
OPP
TAN q =
ADJ 
ADJ

5.  Reciprocal Functions as Ratios of Sides HYP OPP SIN q CSC q OPP HYP=
OPP
HYP
ADJ
HYP
COS q
SEC q =
ADJ
HYP
HYP
OPP
ADJ
OPP
COT q
TAN q =
ADJ
OPP 
ADJ

6.  3 5 4 5 5 3 3 4 4 Trigonometric Functions as Ratios of Sides ex:
SIN q = 5 4
COS q = 5 5 3 3
TAN q = 4  4 A

7. Reference Triangles:
45o 1

8. Reference Triangles:
30o
60o 1 2

9. Trigonometric Identities
ex: Let
Find
Reciprocal Functions
Quotient Identities:
Pythagorean Identities:

10. “Co-functions of complementary angles are equal”
(*complementary = angles adding to 900)
Thanks! So do you!
Luv those shoes
on you!…
Wow you look great! 1 2
Cofunctions:
“Co-functions of complementary angles are equal”

11. Inverse Trig Functions
Basic Idea: Given the value of a trig function - find the angle that produces that value…
ex: 1 2
Notation:
Say: “The inverse sine of 1/2 = /6”
ex: Calculator:
Find  if cos = 0.8 B

12. Solving for Sides 10
530 y
ex:
opp
hyp z
opp
adj 25
420

13. River 
200
400

14. 
40ft
30ft

15. For degree and minute symbol
DMS Format
Stands for Degrees / Minutes / Seconds
Notation: o / //
1’ = 1/60th of a degree
1’’ = 1/60th of a minute (1/3600th of a o)
ex: Convert 152o 15’ 29” into decimal degrees = o
Calculator:
2nd
APPS
For degree and minute symbol

16. ex: Convert 152.258 into DMS format…
ALPHA +
For seconds symbol
ENTER
For answer… o
ex: Convert into DMS format…

17. Evaluating Trig Functions on the Calculator
Set mode to match units of problem OR leave calculator in radian mode and use degree symbol for degree problems.
2. csc / sec / cot = [1/sin] [1/cos] [1/tan]
ex:
sin -76.4o
cot 1.5
sec 5o40’12”

18. HONORS HW
pg 419
#’s 1, 2, 5, 6, all, 15, 16, all, all.
pg 429
1-3 all, 7-10 all, 13, 14, 17, 18, 20, 21, 26, 27, all, 42, 44, 45, 47, 48.