Download Pre-Calculus Unit 2: Trigonometric Functions Parent Letter

Pre-Calculus Unit 2: Trigonometric Functions
Parent Letter
Dear Parents,
Building on standards from Unit 1, students extend their study of the unit
circle and trigonometric functions. Students will create inverses of
trigonometric functions and use the inverse functions to solve trigonometric
equations that arise in real-world problems.
In this unit students will:
 Build upon understanding of the trigonometric functions
 Use special right triangles to determine the x- and y-coordinates of
angles on the unit circle.
 Investigate how the symmetry of the unit circle helps to extend
knowledge to angles outside of the first quadrant
 Use the symmetry of the unit circle to define sine and cosine as
even and odd functions
 Investigate inverse trigonometric function
 Use trigonometric inverses to solve equations and real-world
problems.
Content Connection
McGraw-Hill Pre-Calculus Textbook
Chapter 4 Lesson 1, 3, 6
GA Virtual Learning
http://cms.gavirtualschool.org/Shared
/Math/GSEPrecalculus/TrigonometricF
unctions/index.html
Additional Web Resources
Unit Circle Self-Assessment
http://www.talljerome.com/NOLA/100528_unit
circle.html
Visual Construction of Unit Circle
http://www.mathopenref.com/tocs/constructio
nstoc.html
1.
2.
3.
4.
Essential Questions
How can special right triangles help us find the coordinates of
certain angles on the unit circle?
How does symmetry help us extend our knowledge of the unit
circle to an infinite number of angles?
Why does the calculator only give one answer for an inverse trig
function? Aren’t there infinite answers?
How do inverse trigonometric functions help us solve equations?
Unit Circle
http://www.mathlearning.net/dl2004/Demos/u
nitCircle.html
Unit Circle Formula
http://www.mathwarehouse.com/unitcircle/graph-and-formula-unit-circle.php
Unit Rate & Trigonometric Ratios
Vocabulary
Co-terminal Angle:
Two angles are co-terminal if they are drawn in the standard position and
both have their terminal sides in the same location.
Even Function:
A function f is even if the graph of f is symmetric with respect to the y-axis.
Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f.
Odd Function:
A function f is odd if the graph of f is symmetric with respect to the origin.
Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f.
Reference Angle:
A reference angle for angle θ is the positive acute angle made by the
terminal side of angle θ and the x-axis.
Special Right Triangles:
Refers to the 45-45-90 and 30-60-90 right triangles
Terminal side of angle:
The initial side of an angle lies on the x-axis. The other side, known as the
terminal side, is the one that can be anywhere and defines the angle.
Unit Circle:
A unit circle is a circle that has a radius of one unit.
http://www.mathsisfun.com/algebra/triginteractive-unit-circle.html
Unit Circle History
http://www.math.ucdenver.edu/~jloats/Studen
t pdfs/40_Trigonometry_Trenkamp.pdf
Paul’s Online Notes: Inverse Trig
Functions
http://tutorial.math.lamar.edu/Extras/AlgebraT
rigReview/InverseTrig.aspx
Wolfram: Inverse Trig Functions
http://mathworld.wolfram.com/InverseTrigono
metricFunctions.html
Regent’s Prep: Working w/ Inversion
Trig Functions
http://www.regentsprep.org/regents/math/algt
rig/att8/inversetrig2.htm
Pre-Calculus Unit 2: Trigonometric Functions
Parent Letter
Formulas
45°-45°-90°
30°-60°-90°
Even-Odd Properties
Sample Problems
1.
What is the value of x?
2.
What is the value of s?
3.
Find the values on the interval
𝜋
(− , 𝜋) that satisfies the
2
equation: 𝑆𝑖𝑛−1 (−
Answer: 5 units
4.
𝜋
𝜋
3
3
Answer: 𝑥 = + 2𝜋𝑛; 𝑥 = − + 2𝜋𝑛
)=𝑥
𝑥=
B.
𝑥=−
3
3𝜋
𝜋
4
𝑥=
2
𝑥=0
Answer: B
Answer: 12√2 units
Solve for all values of x. Give a general solution in radians.
1
𝑐𝑜𝑠𝑥 =
2
2
𝜋
A.
C.
D.
√2
5.
Solve for all values of x. Give a general solution in radians.
1
𝑠𝑖𝑛𝑥 = −
2
Answer: 𝑥 =
7𝜋
6
+ 2𝜋𝑛; 𝑥 =
11𝜋
6
+ 2𝜋𝑛