What is the general solution for 2sin(x+pi/4)=1 ?

The general solution for 2sin(x+pi/4)=1 is x=2pin-pi/(12),x=2pin+(7pi)/(12)

Popular >

2sin(x+pi/4)=1

2 sin (x + \frac{π}{4}) = 1

x = 2 πn - \frac{π}{12}, x = 2 πn + \frac{7 π}{12}

Solution steps

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{1}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{1}{2}

x + \frac{π}{4} = \frac{π}{6} + 2 πn, x + \frac{π}{4} = \frac{5 π}{6} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{6} + 2 πn : x = 2 πn - \frac{π}{12}

Solve

x + \frac{π}{4} = \frac{5 π}{6} + 2 πn : x = 2 πn + \frac{7 π}{12}

x = 2 πn - \frac{π}{12}, x = 2 πn + \frac{7 π}{12}

cos (3 x) = \frac{1}{2}

sin (x + \frac{π}{4}) = - \frac{2}{2}, 0 \leq x \leq 2 π

1 + 2 sin^{2} (x) = - 5 cos (x)

sec^{2} (x) tan^{2} (x) + 3 sec^{2} (x) - 2 tan^{2} (x) = 3

2 cos (x) - 3 = 0

What is the general solution for 2sin(x+pi/4)=1 ?
The general solution for 2sin(x+pi/4)=1 is x=2pin-pi/(12),x=2pin+(7pi)/(12)