What is the general solution for sin(x)= pi/4+(0pi)/2 ?

The general solution for sin(x)= pi/4+(0pi)/2 is x=0.90333…+2pin,x=pi-0.90333…+2pin

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sin(x)= pi/4+(0pi)/2

sin (x) = \frac{π}{4} + \frac{0 π}{2}

x = 0.90333 \dots + 2 πn, x = π - 0.90333 \dots + 2 πn

Solution steps

sin (x) = \frac{π}{4} + \frac{0 π}{2}

Simplify

\frac{π}{4} + \frac{0 π}{2} : \frac{π}{4}

Apply trig inverse properties

x = arcsin (\frac{π}{4}) + 2 πn, x = π - arcsin (\frac{π}{4}) + 2 πn

Show solutions in decimal form

x = 0.90333 \dots + 2 πn, x = π - 0.90333 \dots + 2 πn

cos (2 x) - sin (x) - 1 = 0

cos (x) = \frac{5}{20}

cos^{2} (x) + sin^{2} (x) = 2

sin (x) - 3 cos (x) = 1, 0 \leq x \leq 2 π

arccos (θ) = \frac{5}{7}

What is the general solution for sin(x)= pi/4+(0pi)/2 ?
The general solution for sin(x)= pi/4+(0pi)/2 is x=0.90333…+2pin,x=pi-0.90333…+2pin