English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x, 1/6 =cos^2(x)

Solution

solve for

x, \frac{1}{6} = cos^{2} (x)

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn, x = 1.99133 \dots + 2 πn, x = - 1.99133 \dots + 2 πn

Degrees

x = 65.90515 \dots^{\circ} + 36 0^{\circ} n, x = 294.09484 \dots^{\circ} + 36 0^{\circ} n, x = 114.09484 \dots^{\circ} + 36 0^{\circ} n, x = - 114.09484 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{6} = cos^{2} (x)

Switch sides

cos^{2} (x) = \frac{1}{6}

Solve by substitution

cos^{2} (x) = \frac{1}{6}

Let:

cos (x) = u

u^{2} = \frac{1}{6}

u^{2} = \frac{1}{6} : u = \frac{1}{6}, u = - \frac{1}{6}

u^{2} = \frac{1}{6}

For

x^{2} = f (a)

the solutions are

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

u = \frac{1}{6}, u = - \frac{1}{6}

Substitute back

u = cos (x)

cos (x) = \frac{1}{6}, cos (x) = - \frac{1}{6}

cos (x) = \frac{1}{6}, cos (x) = - \frac{1}{6}

cos (x) = \frac{1}{6} : x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

cos (x) = \frac{1}{6}

Apply trig inverse properties

cos (x) = \frac{1}{6}

General solutions for

cos (x) = \frac{1}{6}

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

x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn

cos (x) = - \frac{1}{6} : x = arccos (- \frac{1}{6}) + 2 πn, x = - arccos (- \frac{1}{6}) + 2 πn

cos (x) = - \frac{1}{6}

Apply trig inverse properties

cos (x) = - \frac{1}{6}

General solutions for

cos (x) = - \frac{1}{6}

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

x = arccos (- \frac{1}{6}) + 2 πn, x = - arccos (- \frac{1}{6}) + 2 πn

x = arccos (- \frac{1}{6}) + 2 πn, x = - arccos (- \frac{1}{6}) + 2 πn

Combine all the solutions

x = arccos (\frac{1}{6}) + 2 πn, x = 2 π - arccos (\frac{1}{6}) + 2 πn, x = arccos (- \frac{1}{6}) + 2 πn, x = - arccos (- \frac{1}{6}) + 2 πn

Show solutions in decimal form

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn, x = 1.99133 \dots + 2 πn, x = - 1.99133 \dots + 2 πn

tan (x) + ∣ tan (x) ∣ = 1, - 2 π \leq, x \leq 2 π

2 sin^{2} (x) + 3 sin (x) = 1

11.33 = 1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 12.14

6 cos (3 x) = 6 cos (x)

4 cos (x) = - 22