csc(theta)= 1/x

sec(theta)= 1/ sqrt(1-x^2)
cot(theta)= sqrt(1-x^2)/x

What are these equations used for in real life matters or in regards to calculus?

Can't seem to find the answer anywhere :/

If x = sin(theta), these equations are identities, expressing other trig functions in terms of sin

hey arise from the identity sin^2(theta) + cos^2(theta) = 1

As for real life and calculus, get familiar with the trig functions, and by the time you have mastered the techniques, you will have discovered how they can be used.