# Sinx and cosx relationship test

### The Maclaurin Expansion of cos(x) | The Infinite Series Module

USEFUL TRIGONOMETRIC IDENTITIES. Definitions tanx = sinx cosx secx = 1 cosx cosecx = 1 sinx cotx = 1 tanx. Fundamental trig identity. (cosx). 2. + (sinx). 2. Answer to The relationship in Graph a is defined by y = cos (X) Define a function g to represent the behavior in Graph B b. The re. is, it must pass the Horizontal Line Test. sin x has On the restricted domain –π/ 2 ≤ x ≤ π/2, y = sin x has a x. cos x has an inverse function on this interval.

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- Graphs of trigonometric functions
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## The unit circle definition of sine, cosine, and tangent

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As for finding a formula for the inverse, this is one of those cases where it is not possible. Intuitively, what the inverse sine does in practice is return the angle whose sine is the given value.

### Inverse Sine and Cosine

Indeed, you might read sin-1 x as "the angle whose sine is x? Note that if then the angle that is returned, sin-1 sis a first quadrant angle. While we use the notation sin-1 for the inverse sine function, there are other notations you might see.

The most common ones are arcsin and asin. We shall use both sin-1 and asin. Typically, we use asin in the interactive exercises and demonstrations because of ease of typing and for computer recognition of the function.

### Graphs of trigonometric functions | Trigonometry | Math | Khan Academy

The process is identical to that of defining the inverse sine. The inverse cosine function is denoted as cos-1 which we usearccos, and acos.

The details of the construction of the inverse cosine, as well as the inverse sine, are shown in the demonstration below.

Other notations you might see for the inverse cosine are arccos and acos.

We shall use both cos-1 and acos. As with asin, we use acos in the interactive exercises and demonstrations because of ease of typing and for computer recognition of the function.

## Even and Odd Trig Functions

The following demonstration will take you through the steps of restricting the domain and obtaining the graphs of sin -1 x and cos -1 x. Just follow the instructions on each screen.

After viewing the demonstration we will investigate these functions and their properties further. Inverse Sine and Cosine Defining sin -1 x and cos -1 x Using the procedures above we arrive at definitions for these two inverse trigonometric functions.

For x in the interval [-11], cos -1 x is the angle measure in the interval [0] whose cosine value is x. Radian Measure Although calculators allow inverse sine, cosine and tangent to be applied in radian or degree mode, the actual functions are created using radian measure.