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

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

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cos^2(x)+sin^2(x)=sin(x)+1/2

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}

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

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= 1

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

Switch sides

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

Move

\frac{1}{2}

to the right side

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

Subtract

\frac{1}{2}

from both sides

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

Simplify

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

Simplify

sin (x) + \frac{1}{2} - \frac{1}{2} : sin (x)

sin (x) + \frac{1}{2} - \frac{1}{2}

Add similar elements:

\frac{1}{2} - \frac{1}{2} = 0

= sin (x)

Simplify

1 - \frac{1}{2} : \frac{1}{2}

1 - \frac{1}{2}

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

= \frac{1 \cdot 2}{2} - \frac{1}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 2 - 1}{2}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 1

Subtract the numbers:

2 - 1 = 1

= 1

= \frac{1}{2}

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

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

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

General solutions for

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

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

sin (A) = 0.53

tan (a) = 3, cos (a)

2 sin (2 x) = cos (2 x)

sin (2 θ) = 3

1 2^{2} = 1 5^{2} + 2 0^{2} - 2 (15) (20) (cos (a))

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