Unit Circle Algebra II PDF

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Unit Circle cosine and sine Unit 11 and how...

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NYS COMMON CORE MATHEMATICS CURRICULUM

Homework Packet Mod 2 B

M2

ALGEBRA II

Lesson 7: Problem Set 1.

2.

1.

Graph the sine function on the interval showing all key points of the graph (horizontal and vertical intercepts and maximum and minimum points). Then, use the graph to answer each of the following questions. a.

On the interval , what are the relative minima of the sine function? Why?

b.

On the interval , what are the relative maxima of the sine function? Why?

c.

On the interval , for what values of is ? Why?

d.

If we continued to extend the graph in either direction, what would it look like? Why?

e.

Arrange the following values in order from smallest to largest by using their location on the graph.

f.

On the interval, is the graph of the sine function increasing or decreasing? Based on that, name another interval not included in where the sine function must have the same behavior.

Graph the cosine function on the interval showing all key points of the graph (horizontal and vertical intercepts and maximum and minimum points). Then, use the graph to answer each of the following questions. a.

On the interval , what are the relative minima of the cosine function? Why?

b.

On the interval , what are the relative maxima of the cosine function? Why?

c.

On the interval , for what values of is ? Why?

d.

If we continued to extend the graph in either direction, what would it look like? Why?

e.

What can be said about the end behavior of the cosine function?

f.

Arrange the following values in order from smallest to largest by using their location on the graph.

Use the graph of the sine function given below to answer the following questions.

a.

Desmond is trying to determine the value of . He decides that since is halfway between and that . Use the graph to show him that he is incorrect.

b.

Using the graph, complete each statement by filling in the symbol or . i. ii. iii.

c.

On the interval , list the values of such that .

d.

Explain why there are no values of such that .

Lesson 8: Problem Set

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NYS COMMON CORE MATHEMATICS CURRICULUM

Homework Packet Mod 2 B

M2

ALGEBRA II

1.

Complete the tables below, converting from degrees to radians and back. Where appropriate, give your answers in the form of a fraction of . Degrees

Radians

Radians

Degrees

2.

Use the unit circle diagram from the end of the lesson and your knowledge of the six trigonometric functions to complete the table below. Give your answers in exact form, as either rational numbers or radical expressions.

3.

Use the unit circle diagram from the end of the lesson and your knowledge of the sine, cosine, and tangent functions to complete the table below. Select values of so that .

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NYS COMMON CORE MATHEMATICS CURRICULUM

Homework Packet Mod 2 B

M2

ALGEBRA II

4.

How many radians does the minute hand of a clock rotate through over minutes? How many degrees?

5.

How many radians does the minute hand of a clock rotate through over half an hour? How many degrees?

6.

What is the radian measure of an angle subtended by an arc of a circle with radius if the intercepted arc has length ? How many degrees?

7.

What is the radian measure of an angle formed by the minute and hour hands of a clock when the clock reads 1:30? How many degrees? (Hint: You must take into account that the hour hand is not directly on the .)

8.

What is the radian measure of an angle formed by the minute and hour hands of a clock when the clock reads 5:45? How many degrees?

9.

How many degrees does the earth revolve on its axis each hour? How many radians?

10. The distance from the equator to the North Pole is almost exactly . a. b.

Roughly how many kilometers is degree of latitude? Roughly how many kilometers is radian of latitude?

Lesson 9 Problem Set 1.

For each function, indicate the amplitude, frequency, period, phase shift, horizontal and vertical translations, and equation of the midline. Graph the function together with a graph of the sine function on the same axes. Graph at least one full period of each function. No calculators are allowed. a. b. c. d.

2.

(Hint: First, rewrite the function in the form

For each problem, sketch the graph of the pairs of indicated functions on the same set of axes without using a calculator or other graphing technology. a.

,

b.

,

c.

,

d.

,

e.

,

Lesson 10 Problem Set 1.

For each function, indicate the amplitude, frequency, period, phase shift, horizontal and vertical translations, and equation of the midline. Graph the function together with a graph of the sine function on the same axes. Graph at least one full period of each function. No calculators are allowed.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

NYS COMMON CORE MATHEMATICS CURRICULUM

Homework Packet Mod 2 B

M2

ALGEBRA II

f. g. h. i. j.

(Hint: First, rewrite the function in the form )

Lesson 11 Problem Set 1.

Use your knowledge of function transformation and the graph of to sketch graphs of the following transformations of the tangent function. a. b. c.

2.

Find parameters , , and so that the graphs of and are the same.

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