What is the general solution for -sin(x)+3cos(x-pi/2)=1 ?

The general solution for -sin(x)+3cos(x-pi/2)=1 is x= pi/6+2pin,x=(5pi)/6+2pin

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-sin(x)+3cos(x-pi/2)=1

- sin (x) + 3 cos (x - \frac{π}{2}) = 1

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

Solution steps

- sin (x) + 3 cos (x - \frac{π}{2}) = 1

Rewrite using trig identities

2 sin (x) = 1

Subtract

1

from both sides

2 sin (x) - 1 = 0

Move

1

to the right side

2 sin (x) = 1

Divide both sides by

2

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

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

cos (3 0^{\circ} + u) = 0.8177

cos (x - \frac{3 π}{2}) = \frac{1}{2}

1 - 3 cos (2 θ) = 0

x, sin (\frac{π}{x}) = y - 1

cos (\frac{3 θ}{2}) = 0

What is the general solution for -sin(x)+3cos(x-pi/2)=1 ?
The general solution for -sin(x)+3cos(x-pi/2)=1 is x= pi/6+2pin,x=(5pi)/6+2pin