The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) include the domain, range, period, asymptotes and amplitudes. The domain of a cosine and sine function is all real numbers and the range is -1 to 1. The period is 2π, and the amplitude is 1. They have no asymptotes. The domain of tangent is all real numbers except for π2+kπ. The range is all real numbers and the period is π. Tan has no amplitude and has asymptotes when x= π2+kπ.

The domain of a secant function is all real numbers except for π2+kπ. The domain of a cosecant function is all real numbers except for kπ. The range of both is (-∞.-1]U[1,∞) and the period is 2π. Secant has asymptotes when x=π2+kπ. Cosecant has asymptotes when x=kπ. They have no amplitude. Cotangent’s domain is all real numbers except for kπ. The range is all real numbers and the period is π. It has no amplitude and has asymptotes when x=kπ.

In an inverse function, the x coordinate, or the domain, and the y coordinate, the range, switch places. Since only one to one functions have inverses, we take the interval -π2 to π2, which contains all the possible values of the sine function. Now, the new domain is [-π2, π2], while the range stays the same. We then switch the domain and the range, so the domain and range of arcsin (x) is [-1,1] and [-π2, π2]. For cosine, the interval [0,π] contains all possible values, and the range is still [-1,1]. To find arcos (x) we invert the domain and range again, to get [-1,1] as the domain and [0,π] as the range. For arctan (x), the interval (-π2, π2) includes all possible values. The range still remains all real numbers. Exchanging the domain and range gives us all real numbers as the domain and (-π2, π2) as the range.

As you can see, the properties of the six trig functions have many similarities and the inverse trig functions’ domain and range can be obtained with the one to one property of inverse functions...

...Tracy Gitonga
Modeling Data With Trigonometric Functions
Precalculus 1113-213
October 18, 2011
Real-life math is used in many activities that people do in a daily basis. In the next few paragraphs I will be explaining how to use a real world data and model it with a sine function of the form of y= a sin K (x-b). The graphs will use the law of sine which is defines as, “a law stating that the ratio of the sine of an arc of a spherical triangle to the sine of...

...
PROPERTIES OF SINE AND COSINE FUNCTIONS:
1. The sine and cosine functions are both periodic with period 2π.
2. The sine function is odd function since it’s graph is symmetric with respect to the origin, while the cosine function is an even function since it’s graph is symmetric with respect to y axis.
3. The sine functions:
a. Increasing in the intervals[0, π/2]and...

...Properties of Trigonometric Functions
The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x)are discussed. These include the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points.
Sine Function: f(x) = sin (x)
* Graph
* Domain: all real numbers
* Range: [-1 , 1]
* Period = 2pi
* x-intercepts: x = k pi ,...

...Properties and Functions of Ingredients in Baking
With simple ingredients such as flour, sugar, eggs, milk, butter, and flavorings a wide almost endless of products can be made. But to produce perfect quality products, careful attention must be paid to the ingredients in the recipe. Baking products depend on precise preparation. Baking is not an art. It is a science. It is important to follow baking formulas carefully and completely. “Different flours, fats,...

...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...

...Trigonometric Functions Table
Function
Right Triangle Definition
Unit Circle Definition
Sine
Sine of theta is opposite over hypotenuse Sin θ =o/h
A unit circle is a circle with a radius of 1. In a unit circle sine of θ = y/r. r =1 so sin θ= y
Cosine
Cosine of theta is adjacent over hypotenuse Cos θ =a/h
A unit circle is a circle with a radius of 1. In a unit circle, cosine of θ = x/r. r = 1 sp cos θ = x
Tangent
Tangent of theta is opposite over...

...RUNNING HEAD: AQUARIUM DIFFERENCES 1
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AQUARIUM DIFFERENCES 2
Freshwater vs. Saltwater Comparison
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...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...

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