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

The general solution for cos(x)=(sin(x))/2 is x=1.10714…+pin

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

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

x = 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{cos ( x )}{cos ( x )} = \frac{\frac{s i n ( x )}{2}}{cos ( x )}

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

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

Switch sides

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

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

Multiply both sides by

2

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

Multiply both sides by

2

\frac{2 tan ( x )}{2} = 1 \cdot 2

Simplify

tan (x) = 2

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (2) + πn

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

sin (θ) = - sin (θ) cos (θ)

cos (x) + 3 sin (x) = 0

sin (x) = \frac{2}{25}

4 + tan (x) = 5 cot (x)

3 (sin (x) - 2) (4 cos (x) - 2) = 0

What is the general solution for cos(x)=(sin(x))/2 ?
The general solution for cos(x)=(sin(x))/2 is x=1.10714…+pin