(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the general solution of:

a) sin x = 1/[tex]\sqrt{2}[/tex]

b) cos x = 0.5

3. The attempt at a solution

a) x = asin(1/[tex]\sqrt{2}[/tex])

x = (π/4) + 2nπ

b) x = acos(0.5)

x = π/3 + 2nπ

Basically, my strategy was to solve for the basic angle, and then add multiples of the period (2nπ for sin and cos, nπ for tan).

However, the answers provided are:

a) x = 2nπ + asin(1/[tex]\sqrt{2}[/tex])

or x = (2n+1)π - asin(1/[tex]\sqrt{2}[/tex])

b) 2nπ ± acos(1/2)

Just wondering,

for a) how do they find the second solution x = (2n+1)π - asin(1/[tex]\sqrt{2}[/tex])? I'm curious to know, as the follow on question asks for the first 2 positive solutions to sin x = 1/[tex]\sqrt{2}[/tex], which can apparently only be obtained using both answers shown above. I only know how to get the first solution

for b) where does the ± come from? My answer is the same but for ±.

thanks in advance

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# Homework Help: General solution of trig functions

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