Sine, Cosine, and Tangent Functions
Essential Questions: What is a function? How is the sine definition different from the sine function? Cosine? Tangent? From the graph of these functions, list some properties that describe them? Rebecca Adcock, a former student of EMAT 6690 at The University of Georgia, and I agree that the concept of the Sine, Cosine Functions will occur at lesson 6 of a beginning trigonometry unit. I praise her and her work because I want to use her thoughts on this particular lesson and build upon it with the tangent function.

Please notice what we mean by a function and connecting this with the values along the unit circle.
After Rebecca’s lesson, you should know exactly what the sine and cosine functions look like. Below is a summary of this information.
Sine Function

[pic]

Notice that the sine goes through the origin and travels to a maximum at (π/2, 1). Then, it travels down through (π, 0) to a minimum at (3π/2, -1). Finally the sine travels back up to (2π, 0). Then the sine wave will continue this same process again. Thus, the period of the sine function is 2π. Its amplitude is 1. Recall that sin (-x) = -sin x. This means that the sine function is odd, or it is symmetric to the origin.

Cosine Function

[pic]

Notice that the cosine goes through (0, 1), its maximum, to (π/2, 0) and down to (π, -1), its minimum. The cosine then travels back up through (3π/2, 0) and to (2π, 1). Then the cosine wave will continue this same process again. Thus, the period of the cosine function is also 2π. Its amplitude is 1. Recall that cos (-x) = cos x. This means that the cosine function is even, or it is symmetric to the y-axis.

Student Activity:
1. Give the domain and range of the sine and cosine functions. 2. What are the maximum and minimum values of these functions? 3. Identify the y-intercept and zeros of each function.
4. Identify which function is odd and which one is even....

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PROPERTIES OF SINE AND COSINEFUNCTIONS:
1. The sine and cosinefunctions are both periodic with period 2π.
2. The sinefunction is odd function since it’s graph is symmetric with respect to the origin, while the cosinefunction is an even function since it’s graph is symmetric with respect to y axis.
3. The...

...improve its throughput and power keeping the constraints in mind. This paper summarizes the CORDIC architectures, presents a simulation of basic CORDIC cell and Implements Unfolded CORDIC Architecture on Spartan XC3S50 FPGA family. Keywords— CORDIC, Sine, Cosine, FPGA, CORDIC throughput
III. In Section IV we discuss the implementation of CORDIC algorithm in an FPGA and the simulation of basic CORDIC cell using Xilinx tool and XC3S50 Spartan3 family of FPGA is...

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CENTRAL INSTITUTE OF TECHNOLOGY, KOKRAJHAR
(Centrally Funded Institute under MHRD, Govt. of India)
KOKRAJHAR::783370:: BODOLAND
Estd. :: 2006
A
Project Report
On
SINE AND COSINEFUNCTION GENERATOR
USING VHDL
Submitted by,
DHARMESWAR BORO
ROLL NO: Gau-c-10/L-322....

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Law of sines
In trigonometry, the law of sines (also known as the sine law, sine formula, or sine rule) is anequation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law,
where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the...

...Section 5.2 Trigonometric Functions of Real Numbers
The Trigonometric Functions
EXAMPLE: Use the Table below to ﬁnd the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2
1
EXAMPLE: Use the Table below to ﬁnd the six trigonometric functions of each given real number t. π π (a) t = (b) t = 3 2 Solution: (a) From the Table, we see that the terminal point determined by √ t = √ is P (1/2, 3/2). Since...

...CIRCULAR FUNCTIONS
A different name of an angle is circular functions. Communicate the direction of a triangle to the length of the surface of a triangle. Trigonometric functions are important of triangles and form episodic occurrence, along with many complementary applications. Trigonometric functions have a wide range of uses including calculating indefinite lengths along with angles in triangles.
Trigonometric functions...

...C H A P T E R
16
Circular Functions
Objectives
To use radians and degrees for the measurement of angle. To convert radians to degrees and vice versa. To define the circular functionssine, cosine and tangent. To explore the symmetry properties of circular functions. To find standard exact values of circular functions. To understand and sketch the graphs of circular functions.
16.1...

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all inputs are variable
3.1 The Production Function
Production function is a tool of analysis used in explaining the input-output relationship.
It describes the technical relationship between inputs and output in physical terms. In its
general form, it holds that production of a given commodity depends on certain specific
inputs. In its specific form, it presents the quantitative relationships between inputs and
outputs. A production function...