Answer to Question #87412 in Trigonometry for Rena

Question

Evaluate arccsc sqrt(2), {pi/6,5pi/6}, {pi/3+-2pi*n,5pi/3+-2pi*n}, pi/3, {pi/4+-2pi*n, 3pi/4+-2pi*n} http://prntscr.com/n65cs6

Answer 1

$$arccsc(\sqrt{2}) = \frac{\pi}{4}$$

or

$$arccsc(\sqrt{2}) = \frac{3\pi}{4}$$

from definition, or you can take this information from this web page (http://www.mathamazement.com/Lessons/Pre-Calculus/04_Trigonometric-Functions/inverse-trigonometric-functions.html). But the sine function has period that equal:

$$2\pi$$

so we need to take into account period of function multiplied by integer. So final result is:

$$\{ \frac{\pi}{4} \pm 2\pi n, \frac{3\pi}{4} \pm 2\pi n \}$$