Download Trigonometry

Year: 2014-15
Teacher:
CORE Trigonometry (SEM)
Course: Trigonometry (SEM)
Graphs and
Functions ~
Standards
Month: All Months
In this unit we will explore how to find the distance between two points and the mid-point of a line segment. We will also identify the
important part of circles and how they relate to their respective equations.
Essential Questions
Assessments
Skills
Content
Lessons
Resources
G-GPE.7-Use coordinates to compute
What is the distance between
Quiz 1-1 - 1-2 9/1/2014
Use the distance formula
Distance
perimeters of polygons and areas of
two points on the coordinate plan
Quiz
Special
Right
Use
the
midpont
formula
Midpoint
triangles and rectangles, e.g., using the
Triangles 9/15/2014
distance formula.
Write the standard form of
Circles and their
G.2.1.1-Solve problems involving right
the equation of a circle
equations
What is the midpoint between
triangles.
Graph a circle
G-GPE.1-Derive the equation of a circle of two points on a coordinate plan?
given center and radius using the
Work with the general form of
How can you find the missing
Pythagorean Theorem; complete the
the equation of a circle
sides in a 45-45-90 triangle when
square to find the center and radius of a
given just one side?
circle given by an equation.
G-SRT.8-Use trigonometric ratios and the
Pythagorean Theorem to solve right
How can you find the missing
triangles in applied problems.
G-SRT.9-(+) Derive the formula A = 1/2 ab sides of a 30-60-90 triangle when
sin(C) for the area of a triangle by drawing given just one side?
an auxiliary line from a vertex
perpendicular to the opposite side.
Trigonometric
Functions ~
Standards
In this section we will the basics of trig. We will learn how to convert from degrees to radians and vice versa. We will learn the unit circle
values and how to apply that information. We will work with transformations in order to graph different trig functions.
Essential
Questions
Assessments Skills
F-TF.1-Understand radian measure of an angle as the
1. To convert from
Quiz 2-1 - 2-2
length of the arc on the unit circle subtended by the
degree to radians what 10/1/2014
angle.
is the conversion
Quiz 2-3 - 2-4
F-TF.2-Explain how the unit circle in the coordinate
factor?
10/14/2014
plane enables the extension of trigonometric functions
to all real numbers, interpreted as radian measures of
Quiz 2-6
2. In a 30-60-90 right
angles traversed counterclockwise around the unit
10/21/2014
triangle, the
circle.
hypotenuse is what
Chapter 2 Test
F-TF.3-(+) Use special triangles to determine
times the shortest side?
10/31/2014
geometrically the values of sine, cosine, tangent for ?/3,
?/4 and ?/6, and use the unit circle to express the
3. What does the
values of sine, cosines, and tangent for x, ? + x, and 2?
coefficient in front of the
– x in terms of their values for x, where x is any real
trig function affect?
number.
F-TF.4-(+) Use the unit circle to explain symmetry (odd
4. What does the
and even) and periodicity of trigonometric functions.
coefficient in front of the
F-TF.5-Choose trigonometric functions to model
x in a trig function
periodic phenomena with specified amplitude,
affect?
frequency, and midline.
1. Convert between degrees and degrees,
minutes, and seconds.
2. Convert between degrees and radians.
3. Calculate the arc length and area of a
sector.
4. Review special right triangles.
5. Calculate unit circle values.
6. Determine the domain and range of trig
functions.
7. Calculate trig values when in different
quadrants.
8. Using trig identities, calculate values.
9. Graph using transformations.
10. Calculate the amplitude, fundamental
period, and phase shifts of sinusoidal curves.
11. Write the equation of the graph of a
sinusoidal curve.
12. Sketch the remaining trig functions and
calculate their values.
Content
1. radians
2. conversion
factors
3. unit circle
values
4. trig values
5. graphs of six
trig functions
6. transformations
7. sinusoidal
curves
8. domain and
range
9. equations of
graphs
Lessons Resources
Trigonometry,
Seventh EditionLarson and
Hostetler,
Houghton
Mifflin
F-TF.6-(+) Understand that restricting a trigonometric
function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
F-TF.7-(+) Use inverse functions to solve trigonometric
equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms
of the context.
F-TF.8-Prove the Pythagorean identity sin2(?) +
cos2(?) = 1 and use it to calculate trigonometric ratios.
F-TF.9-(+) Prove the addition and subtraction formulas
for sine, cosine, and tangent and use them to solve
problems.
G-C.1-Prove that all circles are similar.
G-SRT.7-Explain and use the relationship between the
sine and cosine of complementary angles.
G-SRT.8-Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.
5. How do I determine
the fundamental period
from the equation?
6. All the functions
have a fundamental
period of ___, except
for the ____ and _____
function, which have
fundamental periods of
____.
Law of Sines and Law of Cosines
Standards
Essential
Assessments Skills
Questions
F-TF.1-Understand radian measure of an angle as the length of
1. Give one
Quiz 4-1
the arc on the unit circle subtended by the angle.
of the law of
12/1/2014
F-TF.2-Explain how the unit circle in the coordinate plane
sine formulas
Quiz 4-2
enables the extension of trigonometric functions to all real
for area.
12/8/2014
numbers, interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
2. Which law
F-TF.3-(+) Use special triangles to determine geometrically the
has an
values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and use the
ambiguous
unit circle to express the values of sine, cosines, and tangent for
case?
x, ? + x, and 2? – x in terms of their values for x, where x is any
real number.
3. What do we
F-TF.4-(+) Use the unit circle to explain symmetry (odd and
mean by an
even) and periodicity of trigonometric functions.
ambiguous
F-TF.5-Choose trigonometric functions to model periodic
case?
phenomena with specified amplitude, frequency, and midline.
F-TF.6-(+) Understand that restricting a trigonometric function to
4. In order to
a domain on which it is always increasing or always decreasing
use the law of
allows its inverse to be constructed.
cosine we trace
F-TF.7-(+) Use inverse functions to solve trigonometric
what from the
equations that arise in modeling contexts; evaluate the solutions
diagram?
using technology, and interpret them in terms of the context.
F-TF.8-Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and
5. In order to
use it to calculate trigonometric ratios.
use the law of
F-TF.9-(+) Prove the addition and subtraction formulas for sine,
sine to find
cosine, and tangent and use them to solve problems.
area, what do
G-SRT.7-Explain and use the relationship between the sine and
we trace in the
cosine of complementary angles.
diagram?
G-SRT.8-Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.
G-SRT.10-(+) Prove the Laws of Sines and Cosines and use
them to solve problems.
G-SRT.11-(+) Understand and apply the Law of Sines and the
Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
1. Learning and applying the law of sines
Content
1. Law of sines
2. Learning and applying the law of cosines 2. Law of cosines
3. Calculating the area of triangles
4. Drawing, using and applying vectors
3. vectors
Lessons Resources
Law of
sines
Trigonometry,
Seventh EditionLarson and
Hostetler,
Brooks and
Cole
Analytic Trigonometry
Standards
Essential
Assessments
Questions
F-TF.1-Understand radian measure of an angle as the length
1 cos x/2 =
of the arc on the unit circle subtended by the angle.
F-TF.2-Explain how the unit circle in the coordinate plane
2. cos( a -b)=
enables the extension of trigonometric functions to all real
numbers, interpreted as radian measures of angles traversed
3. What does
counterclockwise around the unit circle.
the cos (π/2 F-TF.3-(+) Use special triangles to determine geometrically
x)=
the values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and
use the unit circle to express the values of sine, cosines, and
4. If I'm using
tangent for x, ? + x, and 2? – x in terms of their values for x,
cos 4x
where x is any real number.
= , explain
F-TF.4-(+) Use the unit circle to explain symmetry (odd and
how to find all
even) and periodicity of trigonometric functions.
possible roots
F-TF.5-Choose trigonometric functions to model periodic
for this
phenomena with specified amplitude, frequency, and midline.
equation.
F-TF.6-(+) Understand that restricting a trigonometric function
to a domain on which it is always increasing or always
decreasing allows its inverse to be constructed.
F-TF.7-(+) Use inverse functions to solve trigonometric
equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the
context.
F-TF.8-Prove the Pythagorean identity sin2(?) + cos2(?) = 1
and use it to calculate trigonometric ratios.
F-TF.9-(+) Prove the addition and subtraction formulas for
sine, cosine, and tangent and use them to solve problems.
G-SRT.4-Prove theorems about triangles. Theorems include:
a line parallel to one side of a triangle divides the other two
proportionally, and conversely; the Pythagorean Theorem
proved using triangle similarity.
G-SRT.8-Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied problems.
G-SRT.10-(+) Prove the Laws of Sines and Cosines and use
them to solve problems.
G-SRT.11-(+) Understand and apply the Law of Sines and the
Law of Cosines to find unknown measurements in right and
non-right triangles (e.g., surveying problems, resultant
forces).
Analytic Trig test
12/1/2014
Skills
1. Evaluating trig identities.
2. Verifying trig identities
Quiz on verifications
and simplifications
3. Solving trig equations.
12/1/2014
Trig equation quiz
12/1/2014
angle measure quiz
12/1/2014
4. Learning and applying sum
and difference formulas.
Content
Lessons Resources
1. Verifications
2. Simplifications
3. Trig equations
4. sum and difference
formulas
5. Learning and applying multiple 5. multiple angle formulas
angle and product to sum
formulas.
6. product to sum formulas
Difference Trigonometry,
between a Seventh Editionverification Larson and
and a
Hostetler,
simplification Brooks and
Cole