1.5 Notes.notebook
January 23, 2014
1.5 Right Triangle Trigonometry
Name: __________________
Objectives: Students will be able to evaluate trig functions using
triangles and solve word problems involving angle of elevation and
angle of depression.
S O H - C A H - T
O A
sinθ =
cscθ =
cosθ =
secθ =
tanθ =
cotθ =
Pythagorean Theorem:
a2 + b2 = c2
Jan 7­9:06 AM
45o
o
60
1
√2
1
2
45
30
√3
30-60-90 Triangle
θ
30o
sinθ
Memorize
these!
o
o
1
45-45-90 Triangle
cosθ
tanθ
cscθ
secθ
cotθ
45o
60o
Nov 28­2:28 PM
1
1.5 Notes.notebook
January 23, 2014
Examples: Find the values of the six trig ratios for R.
Rationalize answers.
T
√7 in.
9 in.
S
R
Jan 7­9:22 AM
Solve ΔABC for all of its unknown parts.
B
a
β
α = 41 o , c = 10
c
α
C
b
A
Jan 7­9:23 AM
2
1.5 Notes.notebook
January 23, 2014
Inverse Trig Functions
sin-1x = α
provided
sinα = x
and
-90o ≤ α ≤ 90o
cos-1x = α
provided
cosα = x
and
0o ≤ α ≤ 180o
tan-1x = α
provided
tanα = x
and
-90o ≤ α ≤ 90o
Examples
1.) Find α if cosα = √3/2.
2.) Evaluate sin-1√2/2.
3.) Evaluate tan-1(5.68) with a calculator.
4.) Use a calculator to find α if cosα = 0.923.
Jan 7­9:25 AM
Application Problems
1.) An 18 foot ladder is placed against a wall so that the foot
of the ladder is 7 feet from the base of a wall. How high up
the wall will the ladder reach? What angle does the ladder
make with the ground?
Jan 7­9:29 AM
3
1.5 Notes.notebook
January 23, 2014
2.) Robin Hood plans to use a 30 ft ladder to reach the castle
window of Maid Marian. Little John, who made the ladder, advised
Robin that the angle of elevation of the ladder must be between
55o and 70o for safety. What are the minimum and maximum
heights that can safely be reached by the top of the ladder when
it is placed against the 50 ft castle wall?
Jan 7­9:37 AM
Homework:
Pg. 86: For Thought: #1-10
Pgs 86-88: Exercises: #5-47 odd
Jan 7­9:42 AM
4