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In statics analysis, we use the sine function when dealing with forces that are perpendicular to a reference axis, and the cosine function when dealing with forces that are parallel to the reference axis.

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3mo ago

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What is the derivation of the wave function?

A simple wave function can be expressed as a trigonometric function of either sine or cosine. lamba = A sine(a+bt) or lamba = A cosine(a+bt) where lamba = the y value of the wave A= magnitude of the wave a= phase angle b= frequency. the derivative of sine is cosine and the derivative of cosine is -sine so the derivative of a sine wave function would be y'=Ab cosine(a+bt) """"""""""""""""""" cosine wave function would be y' =-Ab sine(a+bt)


What is a reciprocal trig function?

A reciprocal trigonometric function is the ratio of the reciprocal of a trigonometric function to either the sine, cosine, or tangent function. The reciprocal of the sine function is the cosecant function, the reciprocal of the cosine function is the secant function, and the reciprocal of the tangent function is the cotangent function. These functions are useful in solving trigonometric equations and graphing trigonometric functions.


When is it better to use the sine function and when is it better to use the cosine function when modeling sinusoidal behavior?

The only difference is a phase shift of pi/2 radians (90 degrees), so there is no aprticular advantage in either.


Which angle length does cosine give you?

Sides have lenght, angles do not. Cosine is the ratio of the adjacent side to the hypotenuse. Cosine can be used to find either of these sides if the other is known.


How do you know when to use sine over cosine or cosine over sine?

You can choose either or but tangent which is sin/cos seems to be the most common way.


How do you find out the top angle of an Isosceles triangle if you do not know the base angle?

It depends on whether you know the lengths of all three sides (either explicitly or otherwise). If you don't know the lengths of the sides you cannot find the top angle. If you do know the sides you can apply the cosine rule: cos(A) = (b2 +c2 - a2)/2bc and then use the inverse cosine function to determine A.


When finding the sides and angles of a right triangle when is it necessary to use Trigonometry?

if you have any two sides, you can calculate either of the (non right angle) angles. if you have a (non right angle) angle and one side, you can calculate any other side. you will need either tables, or a scientific calculator with sin / cosine / tangent function


Can cosine graphs continue infinitely in either direction?

Yes!!!! They are cyclic in nature. The cosine wave goes from negative infinity to positive infinity. It has a Wavelength of 2pi(360 degrees) and ranges from -1 to +1 . Similarly the Sine wave.


How do you find the length of a side in a triangle that is not a right triangle?

Use either the Sine or Cosine rules depending on the information you know about the triangle.


How does knowing the zeros of a function help determine where a function is positive?

Knowing the zeros of a function helps determine where the function is positive by identifying the points where the function intersects the x-axis. Between these zeros, the function will either be entirely positive or entirely negative. By evaluating the function's value at points between the zeros, one can determine the sign of the function in those intervals, allowing us to establish where the function is positive. This interval analysis is crucial for understanding the function's behavior across its domain.


What is picards theorem?

In complex analysis, the term Picard theorem (named after Charles Émile Picard) refers to either of two distinct yet related theorems, both of which pertain to the range of an analytic function.


What is partial analysis?

Partial analysis is simply a first view of how something is going. This is an observation done either briefly or less thoroughly than a complete analysis.