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You may have already worked out that what we did here was to find the cosine of the angle by taking the reciprocal of the secant. We then simply applied the arccosine function to the result.
If you have entered the keystrokes correctly, you should now see a display like the one shown below. If you have read the page entitled "The Cosecant Function" you will by now realise that all of the trigonometric functions are very closely interrelated.
No real surprise then, that the similarity between the graphs of the sine and cosine is mirrored by the similarity between the graphs of the cosecant and secant, with the only real difference in both cases being a ninety degree phase difference.
The fact that the trigonometric functions are so closely interrelated means that we can often replace an expression involving one trigonometric function with an equivalent expression involving a different trigonometric function.
This can often be very useful. The secant function, in common with other trigonometric functions, can be represented as an infinite series. The value returned by a trigonometric function for a given angle cannot be calculated using a simple algebraic formula. For most angles, an exact value can only be obtained as the sum of an infinite number of terms, which is obviously impossible to achieve.
A reasonably accurate approximation of the value is found using the sum of a limited number of terms from the function's infinite series.
The greater the number of terms included, the greater the accuracy of the result. The number of terms used will depend on the accuracy required, and on the computational resources available. The sine is useful for describing natural phenomena and for writing Fourier series to describe relations. The cosine, cos x, is the ratio of x to r, the ratio of the horizontal component to the radius. It is useful in describing natural phenomena particularly in writing Fourier series for relations.
Because it is the reciprocal of the sine, when the sine increases the cosecant decreases. When the sine reaches a maximum, the cosecant reaches a minimum. When the cosine is 0, the secant is undefined. When the cosine reaches a relative maximum, the secant is at a relative minimum.
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Elizabeth X. Answer the value of secant is undefined.
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