Question

What is CSC trigonometry?

Answer 1

Hint: First, we need to analyze the given information so that we are able to discuss the problem. Generally, in Mathematics, the trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation and these identities are useful whenever expressions involving trigonometric functions need to be simplified.

Complete step-by-step solution:
Given that CSC means cosecant trigonometry which is the inverse function of the sine value which can be also represented as $\csc \theta = \dfrac{1}{{\sin \theta }}$.
Hence the cosecant is the angle of ratio length of hypotenuse and length of sides opposite angle.
Therefore, $\csc \theta = \dfrac{{Hyp}}{{Opp}}$ where $\csc \theta = \dfrac{{Hyp}}{{Opp}} \Rightarrow \sin \theta = \dfrac{{Opp}}{{Hyp}}$
The reciprocal identity of the trigonometric functions states that three functions can be defined as the reciprocal of the other three functions such that, secant can be defined as cosine, cosecant can be defined as the sine, and cotangent can be defined as the tangent.
Where trigonometric is the branch of mathematics that will deal with the specific function of angles and also their application in the calculation
Additional information:
We shall analyze the given graph first.
Here in the first quadrant, all ratios are positive. In the second quadrant, only sine is positive, and in the third quadrant, only the tangent ratio is positive. And in the fourth quadrant, only the cosine ratio is positive.

When we are given $\sin \left( {90 + \theta } \right)$ , we need to understand $\sin 90$ is in the first quadrant and $\sin \left( {90 + \theta } \right)$is in the second quadrant. In the second quadrant, only the sin ratio is positive and cosine is negative. That’s why we got minus sign in this trigonometric identity $\sin \left( {90 + \theta } \right) = - \cos \theta $

Note: The six basic trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent and all the fundamental trigonometric identities are derived from the six trigonometric ratios.
The trigonometric functions are those real functions that relate the angle to the ratio of two sides of a right-angled triangle.