Question

Without using a calculator, find all the solutions of the trig equation, csc(β)=√2, where −π<β≤π. β= Radians. Give answer(s) in exact form in terms of π. If you get multiple angles, enter them as a list separated by comma. If there are no solutions, enter "DNE".

Name: without using a calculator find all the solutions of the trig equation csc2 where radians give answers in exact form in terms of if you get multiple angles enter them as a list separated by 19529
Uploaded: 2025-05-22T17:29:17-08:00
Duration: 1 min 41 s
Channel: Andrew Noble
Description: without using a calculator find all the solutions of the trig equation csc2 where radians give answers in exact form in terms of if you get multiple angles enter them as a list separated by 19529

          Without using a calculator, find all the solutions of the trig equation,
csc(β)=√2,   where −π<β≤π.
β=   Radians.
Give answer(s) in exact form in terms of π.
If you get multiple angles, enter them as a list separated by comma. If there are no solutions, enter "DNE".

Added by John P.

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Instant Answer

Solved by Expert Andrew Noble

05/22/2025

Step 1

\[ \csc(\beta) = \sqrt{2} \] Since \(\csc(\beta) = \frac{1}{\sin(\beta)}\), this implies: \[ \frac{1}{\sin(\beta)} = \sqrt{2} \implies \sin(\beta) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \] Show more…

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Without using a calculator, find all the solutions of the trig equation, csc(β)=√2, where −π<β≤π. β= Radians. Give answer(s) in exact form in terms of π. If you get multiple angles, enter them as a list separated by comma. If there are no solutions, enter "DNE".