Introduction to Sine and Cosine Functions
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Introduction to Sine and Cosine Functions
1
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Graphic Sinusoid
the graph of any trigonometric function.
Verbal: Related Vocabulary Periodic function is a function whose values repeat at regular intervals.
2
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Cycle the part of the graph from any one point to the point where the graph starts to repeat.
Period is the difference between the horizontal coordinates corresponding to one cycle. (How long does it take the function to start repeating.)
The parent function, the function without any transformations, of sine and cosine has a period of 360 degrees.
3
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Algebraic The function f is a periodic function if and only if there is a number p for which f(x-p)=f(p)
Numeric Do not copy. Follow the directions to create a drawing. 1. Draw a first quadrant angle in standard position. Label the terminal side r. 2. Label the initial side x. 3. Draw a line from the terminal side to the horizontal axis. Label that line y. That is called a reference triangle.
4
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Using that triangle write the value of
and
How do they relate to what you already know about those function?
Definitions
SOH-CAH-TOA 5
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Now let's take a look at the drawing and discuss what is happening to the graph and how it relates to the coordinate plane.
QUADRANT II
SINE
TANGENT QUADRANT III
QUADRANT I
ALL
COSINE QUADRANT IV
ALL STUDENTS TAKE CHEMISTRY 6
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Problems The terminal side of an angle in standard position contains the point (-3,4). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
The terminal side of an angle in standard position contains the point (8,-6). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
7
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
The terminal side of an angle in standard position contains the point (-3,-7). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
The terminal side of an angle in standard position contains the point (-1,-5). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
8
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
What is the sine of theta if theta equals 180 degrees? Prove it! The calculator told me is not proof!!!!
9
(3) Intro Sine and Cosine
Introduction to Sine and Cosine Functions
1
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Graphic Sinusoid
the graph of any trigonometric function.
Verbal: Related Vocabulary Periodic function is a function whose values repeat at regular intervals.
2
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Cycle the part of the graph from any one point to the point where the graph starts to repeat.
Period is the difference between the horizontal coordinates corresponding to one cycle. (How long does it take the function to start repeating.)
The parent function, the function without any transformations, of sine and cosine has a period of 360 degrees.
3
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Algebraic The function f is a periodic function if and only if there is a number p for which f(x-p)=f(p)
Numeric Do not copy. Follow the directions to create a drawing. 1. Draw a first quadrant angle in standard position. Label the terminal side r. 2. Label the initial side x. 3. Draw a line from the terminal side to the horizontal axis. Label that line y. That is called a reference triangle.
4
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Using that triangle write the value of
and
How do they relate to what you already know about those function?
Definitions
SOH-CAH-TOA 5
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Now let's take a look at the drawing and discuss what is happening to the graph and how it relates to the coordinate plane.
QUADRANT II
SINE
TANGENT QUADRANT III
QUADRANT I
ALL
COSINE QUADRANT IV
ALL STUDENTS TAKE CHEMISTRY 6
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
Problems The terminal side of an angle in standard position contains the point (-3,4). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
The terminal side of an angle in standard position contains the point (8,-6). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
7
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
The terminal side of an angle in standard position contains the point (-3,-7). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
The terminal side of an angle in standard position contains the point (-1,-5). Sketch the angle in standard position and find the sine, cosine and tangent of the angle.
8
Unit 2 - Circular Functions
(3) Intro Sine and Cosine
What is the sine of theta if theta equals 180 degrees? Prove it! The calculator told me is not proof!!!!
9
