What is the general solution for cos(x/2)=-0.4 ?

The general solution for cos(x/2)=-0.4 is x=2*1.98231…+4pin,x=-2*1.98231…+4pin

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cos(x/2)=-0.4

cos (\frac{x}{2}) = - 0.4

x = 2 \cdot 1.98231 \dots + 4 πn, x = - 2 \cdot 1.98231 \dots + 4 πn

Degrees

x = 227.15635 \dots^{\circ} + 72 0^{\circ} n, x = - 227.15635 \dots^{\circ} + 72 0^{\circ} n

Solution steps

cos (\frac{x}{2}) = - 0.4

Apply trig inverse properties

cos (\frac{x}{2}) = - 0.4

General solutions for

cos (\frac{x}{2}) = - 0.4

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

\frac{x}{2} = arccos (- 0.4) + 2 πn, \frac{x}{2} = - arccos (- 0.4) + 2 πn

\frac{x}{2} = arccos (- 0.4) + 2 πn, \frac{x}{2} = - arccos (- 0.4) + 2 πn

Solve

\frac{x}{2} = arccos (- 0.4) + 2 πn : x = 2 arccos (- 0.4) + 4 πn

\frac{x}{2} = arccos (- 0.4) + 2 πn

Multiply both sides by

2

\frac{x}{2} = arccos (- 0.4) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = 2 arccos (- 0.4) + 2 \cdot 2 πn

Simplify

x = 2 arccos (- 0.4) + 4 πn

x = 2 arccos (- 0.4) + 4 πn

Solve

\frac{x}{2} = - arccos (- 0.4) + 2 πn : x = - 2 arccos (- 0.4) + 4 πn

\frac{x}{2} = - arccos (- 0.4) + 2 πn

Multiply both sides by

2

\frac{x}{2} = - arccos (- 0.4) + 2 πn

Multiply both sides by

2

\frac{2 x}{2} = - 2 arccos (- 0.4) + 2 \cdot 2 πn

Simplify

x = - 2 arccos (- 0.4) + 4 πn

x = - 2 arccos (- 0.4) + 4 πn

x = 2 arccos (- 0.4) + 4 πn, x = - 2 arccos (- 0.4) + 4 πn

Show solutions in decimal form

x = 2 \cdot 1.98231 \dots + 4 πn, x = - 2 \cdot 1.98231 \dots + 4 πn

tan (x - 4 5^{\circ}) - tan (x + 4 5^{\circ}) = 4

sin (x) (2 sin^{2} (x) - 1) = 0

sin (2 x) = 10 cos (x)

- 2 cos (3 θ) = 1, 0 \leq θ \leq 2 π

cos (a) = 0.998482

What is the general solution for cos(x/2)=-0.4 ?
The general solution for cos(x/2)=-0.4 is x=2*1.98231…+4pin,x=-2*1.98231…+4pin