EX3:
g(x) =
1
1
sin
x .
2
2
y
x
EX4: Write an equation satisfying the following conditions
A sine function with an amplitude of and a period of 180 degrees.
A cosine function with an amplitude of 8 and a period of 600 degrees.
13
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1/1
C
Patterns in the unit circle: sin2 +cos2 = _
Opposites Theorem:
cos (-)=_
sin (-)=_
tan (-)=_
Supplements Theorem:
sin(- )=_
cos ( - ) = _
tan ( - ) = _
Complements Theorem:
sin (
/2 - )=_
cos (
/2 - )=_
Half-Turn Theorem:
cos(+)=_
sin ( + ) = _
tan ( + )
QUIZ REVIEW
Algebra 2H Ch. 13
Topics on the quiz:
1. Solve problems using the 6 trig functions
2. Arc length and area of a sector (know formulas and how to use them)
3. Converting from degrees to radians and radians to degrees
4. Law of Sines and Law of C
Unit Circle Assignment Day 2
Name_
In 1 - 10, which quadrant would the following angle be found?
1. 68
6.
2.
42
5
7
3
3. 210
7. 225
8.
4.
93
6
13
3
9. 170
5. -123
10. -324
In 11 - 22, tell whether the answer is positive (pos) or negative (neg).
12
11. c
Problem Set 1
1. A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is
closest to how much the gas would cost for this car to travel 2,727 typical miles?
A.$ 44.44
B.$109.08
C.$118.80
D.$408.04
E.$444.40
2 .When x =
Problem Set 2
1. The lead of a screw is the distance that the screw advances in a straight line when the screw is
turned 1 complete turn. If a screw is 2 inches long and has a lead of
complete turns would get it all the way into a piece of wood?
A. 5
B.10
Alg 2 H
13-3 The Unit Circle
unit circle -
The unit circle has a center at ( _ , _) and a radius of _
The Unit circle contains the two special right triangles (30 -60 -90 and the 45 -45 -90 )
3
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1/2
Ch 13-14 Notes.pdf (3/19)
y
1
1
1
x
1
Solving Equations Involving Trigonometric Functions
*Always pay attention to whether the question asks for degrees or radians. If you use our calculator make sure you are in the right mode.*
1. Evaluating Values of
Inverse Trig. Functions
3. Find all poss
EX3: Write a sine function for the set of conditions.
Phase shift of 60 degrees to the right and a vertical shift down 4 units
EX4: Write a cosine function for the set of conditions.
A vertical shift up 6 units and a phase shift of 180 to the left.
11
201
Algebra 2 STEM Chapter
13.1 Worksheet
Right Triangle Trigonometry
Name: _
1. Find RQ and PR for each of the triangles below.
A
2.
B
Find x and y for each of the triangles below.
A
B
y
x
y
C
x
x
y
1
3. Find the value of x and y in the triangles below.
A
4
Alg 2 STEM
13.3 Degrees and Radians
Lengths of Arcs and Areas of Sectors
radian:
How to convert from degrees to radians and radians to degrees:
a) If you have an angle measured in degrees,_
b) If you have an angle measured in radians, _
EX1: Convert degre
Algebra 2 STEM
13-1 Right Triangle Trigonometry
In a RIGHT triangle the lengths of the three sides are related by the Pythagorean Theorem.
What is the Pythagorean Theorem?
(label the picture)
_
hypotenuse of a right triangle:_
relative to angle
:
side adj
Alg 2 H
14-1 Graphs of Sine and Cosine
Day 1
periodic function functions that repeat at regular intervals
cycle a regular interval
period length of one cycle
1
amplitude: amp = (max min) : always positive
2
frequency is the number of cycles/time or the re
SINE
1st answer- based
on restriction
COSINE
TANGENT
From Calc or Unit
circle
From Calc or unit circle
From Calc or unit circle
0
/ 2 / 2
2
/ 2 / 2
2nd answer
General solution
(all real numbers)
_+ 2 n, n is an _+ 2 n, n is an
integer
integer
_+ n
13.5/13.6
Law of Sine and Cosine
Algebra 2H
WHEN TO USE:
LAW OF COSINES
LAW OF SINES
EX1: Find EF
EX2: Find AB
1
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1/2
Ch 13-14 Notes4th.pdf (1/19)
EX3:Solve the triangle. (Find AB first)
EX4: Find m R
2
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2/2
Ch 13-14
Alg 2 H
13-4/14-6 Solving Trig Functions Using Inverses
Day 1
inverse sine function
sin 1 or Arcsin
inverse cosine function
cos 1 or Arccos
inverse tangent function
tan 1 or Arctan
-INVERSE RELATION
FUNCTION
sin = a
sin 1 a =
cos = a
cos 1 a =
tan = a
tan
Sine and Cosine Graphs Investigation
1. go to http:/www.geogebratube.com/student/m13795
click on go to student worksheet
2. begin with display sine function checked
What do you notice about the sine function graph? (What values are possible outputs?
What
EX4:
Find all possible values in radians.
A
B
1
2
cos-1
sin-1
= _
3
2
= _
Ex 5: Solve for . (degrees)
C cos
1st answer- based
on restriction
= .8
SINE
From Calc or Unit
circle
/2
/2
2nd answer
General solution
(all real numbers)
COSINE
From Calc or unit
c
14.1 Day 2 page 995 #1-7, 14-17, 25, 26, 33, 39
Name:_
1.
2.
3.
4.
y
Amplitude:
Period:
x
y
5.
Amplitude:
Period:
x
y
6.
Amplitude:
Period:
x
y
7.
Amplitude:
Period:
Hertz:
x
y
14.
Amplitude:
Period:
x
y
15.
Amplitude:
Period:
x
y
16.
Amplitude:
Period:
x