Solving for Angle 'a' in Quadrant 2: Math Homework

[Random-Hero-]

Homework Statement

Given that (csc a) = (sec0.75) and that 'a' lies in the second quadrant, determine the measure of angle 'a', to two decimal places.

Homework Equations

reciprocal and quotient identities.

The Attempt at a Solution

I only got as far as:

1/sin(a) = 1/cos(0.75)

The answer in the back of the book is 2.32

Can anyone guide me towards the light? thanks in advance!

 

[HallsofIvy]

Well, it is not difficult to find that cos(.75)= .7317 using a calculator and , again using a calculator, that sin(a)= .7317 for a= .8208. Of course, that is the "principal root", less than $\pi/2$. Since a is in the second quadrant, a= $\pi$- .8208= 2.3208