30 April 2012 Geometry
Put all papers from folder in your binder.
Warm Up
1) Find x.
x
tan 39 
125
29
cos 52 
x
HOMEWORK DUE TUESDAY: pg. 645: 1 – 20
FINAL PROJECT DUE MAY 8
Objective
Students will use
sine, cosine and tangent ratios and their inverses to
solve problems.
Students will take notes and solve problems.
Right Triangle Vocabulary
Adjacent
hypotenuse- the longest side
leg adjacent- the side that is not the
hypotenuse that helps form the angle;
adjacent means “next to”
ANGLE
leg opposite- the side
that does not help form the
angle; side “across” the
triangle
Opposite
Sine, Cosine and Tangent are special ratios
defined as follows:
WRITE
SOH CAH TOA
THESE
DOWN
Sine = “sin” =
Cosine = “cos” =
Tangent = “tan” =
solving equations with trig
functions
1) Strategy– rewrite the trig function as a
decimal and solve for the unknown value
ex: sin 42  x  sin 42⁰ ≈ 0.6691
20
x
0.6691 =
20
20 (0.6691) = x
x = 13. 3826
solving equations with trig
functions
2) remember sinϴ, cosϴ, tanϴ are RATIOS
YOU CAN NOT DIVIDE
the angle measure to simplify!!!
sin 30
 sin
30
STRATEGY– use parenthesis to help you remember!
x
sin 42 
20
20 (sin 42⁰) = x
20 (0.6691) = x
x = 13.2826
multiply both sides by 20
use calculator
How do you know which ratio to use?
1) Identify H, A and O.
2) What information do you have? What
information do you need to find?
3) Use the trig ratio with “have/need” sides.
DO Handout- TRIG Worksheet 3- Calculating Sides
Inverse trigonometric functions UNDO trig
functions:
“inverse cosine”  cos-1 (cos ϴ) = ϴ
“inverse sine” sin-1 (sin ϴ) = ϴ
“inverse tangent”  tan-1 (tan ϴ) = ϴ
As with ANY ALGEBRA- if you do it to one side,
you must ALSO DO IT TO THE OTHER!
If you know the RATIO of sides,
you can use the INVERSE Trig functions
to find the ANGLES!!
example
Find ϴ:
ϴ
9
First, mark H, O and A.
What information do you KNOW?
What trig function
H
can you use?
6
tan ϴ = O/A
tan ϴ = 6/9
tan -1(tan ϴ) = tan -1 (6/9)
Use inverse tangent, because you need to find
the angle! ϴ = tan-1 (6/9) = 33.6901◦
practice
Do Trigonometry Worksheet T4
- Calculating Angles
Each group will be asked to put one solution on
a white board and be prepared to share their
work with the class.
debrief
Why do the trig ratios remain equivalent for any
acute angle, no matter how big the triangle?
How do you know which trig function to use
when solving trig problems?