Question

How do you use special angles to find the ratios of csc 315 degrees?

Answer 1

`315^@ = 45^@` less than a full circle
`color(white)("XXX")`i.e. `315^@-= -45^@`
`csc(-45^@) =1/sin(-45^@)=-1/sin(45^@)= -sqrt(2)`

Explanation:

Since `(-45^@)` is in Quadrant IV, `sin` (and therefore `csc`) is negative.

The `45^@` angle is a no-right angle in a right-angled equilateral triangle. If the equal length arms of the triangle are of length 1, then the hypotenuse is of length `sqrt(2)` (Pythagorean Theorem).

`sin = ("opposite")/("hypotenuse")`