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Popular >

4cos(x^2)-1=0

Solution

4 cos (x^{2}) - 1 = 0

Solution

x = 1.31811 \dots + 2 πn, x = - 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn, x = - 2 π - 1.31811 \dots + 2 πn

+1

Degrees

x = 0^{\circ} + 157.96708 \dots^{\circ} n, x = 0^{\circ} - 157.96708 \dots^{\circ} n, x = 0^{\circ} + 192.16097 \dots^{\circ} n, x = 0^{\circ} - 192.16097 \dots^{\circ} n

Solution steps

4 cos (x^{2}) - 1 = 0

Move

1

to the right side

4 cos (x^{2}) - 1 = 0

Add

1

to both sides

4 cos (x^{2}) - 1 + 1 = 0 + 1

Simplify

4 cos (x^{2}) = 1

4 cos (x^{2}) = 1

Divide both sides by

4

4 cos (x^{2}) = 1

Divide both sides by

4

\frac{4 cos ( x ^{2} )}{4} = \frac{1}{4}

Simplify

cos (x^{2}) = \frac{1}{4}

cos (x^{2}) = \frac{1}{4}

Apply trig inverse properties

cos (x^{2}) = \frac{1}{4}

General solutions for

cos (x^{2}) = \frac{1}{4}

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

x^{2} = arccos (\frac{1}{4}) + 2 πn, x^{2} = 2 π - arccos (\frac{1}{4}) + 2 πn

x^{2} = arccos (\frac{1}{4}) + 2 πn, x^{2} = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

x^{2} = arccos (\frac{1}{4}) + 2 πn : x = arccos (\frac{1}{4}) + 2 πn, x = - arccos (\frac{1}{4}) + 2 πn

x^{2} = arccos (\frac{1}{4}) + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = arccos (\frac{1}{4}) + 2 πn, x = - arccos (\frac{1}{4}) + 2 πn

Solve

x^{2} = 2 π - arccos (\frac{1}{4}) + 2 πn : x = 2 π - arccos (\frac{1}{4}) + 2 πn, x = - 2 π - arccos (\frac{1}{4}) + 2 πn

x^{2} = 2 π - arccos (\frac{1}{4}) + 2 πn

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

x = 2 π - arccos (\frac{1}{4}) + 2 πn, x = - 2 π - arccos (\frac{1}{4}) + 2 πn

x = arccos (\frac{1}{4}) + 2 πn, x = - arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn, x = - 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = - 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn, x = - 2 π - 1.31811 \dots + 2 πn

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