Question

What is the secant of $270$ degrees?

Answer 1

Hint: Trigonometry is a branch of mathematics that investigates the relationship between a right-angled triangle's angles and sides. For six trigonometric functions, a relationship between sides and angles is defined.

Complete step-by-step solution:
The relationship between the angles and sides of a right-angled triangle is studied in this branch of mathematics. There are six different types of trigonometric functions. A trigonometric function can be expressed in terms of its trigonometric counterparts, in this case the trigonometric counterparts are the other trigonometric functions.
The secant of an angle is a trigonometric function. The secant of an angle is calculated by the length of the hypotenuse divided by the length of the adjacent side in a right triangle. It is abbreviated as 'sec' in a formula.
The secant of an angle can also be represented as one divided by the cosine of the same angle.
$\sec \theta = \dfrac{1}{{\cos \theta }}$
Here $\theta $ represents the given angle.
According to the question, we need to find the secant of $270$degrees , $\sec ({270^ \circ })$.
We know that $\sec ({270^ \circ }) = \dfrac{1}{{\cos ({{270}^ \circ })}}$
It is known that $\cos ({270^ \circ }) = 0$.
This means that the secant of $270$degrees will have zero in its denominator. Resulting in a value that is not defined.
Thus, the secant of $270$ degrees is not defined.

Note: Trigonometric functions have a wide range of applications in our daily lives. In the analysis of periodic functions, such as sound and light waves, the sine and cosine functions are crucial. Trigonometry and algebra are the crucial concepts that make up Calculus.