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Popular >

0.6=cos^2(x)

Solution

0.6 = cos^{2} (x)

Solution

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

+1

Degrees

x = 39.23152 \dots^{\circ} + 36 0^{\circ} n, x = 320.76847 \dots^{\circ} + 36 0^{\circ} n, x = 140.76847 \dots^{\circ} + 36 0^{\circ} n, x = - 140.76847 \dots^{\circ} + 36 0^{\circ} n

Solution steps

0.6 = cos^{2} (x)

Switch sides

cos^{2} (x) = 0.6

Solve by substitution

cos^{2} (x) = 0.6

Let:

cos (x) = u

u^{2} = 0.6

u^{2} = 0.6 : u = 0.6, u = - 0.6

u^{2} = 0.6

For

x^{2} = f (a)

the solutions are

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

u = 0.6, u = - 0.6

Substitute back

u = cos (x)

cos (x) = 0.6, cos (x) = - 0.6

cos (x) = 0.6, cos (x) = - 0.6

cos (x) = 0.6 : x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

cos (x) = 0.6

Apply trig inverse properties

cos (x) = 0.6

General solutions for

cos (x) = 0.6

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

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn

cos (x) = - 0.6 : x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

cos (x) = - 0.6

Apply trig inverse properties

cos (x) = - 0.6

General solutions for

cos (x) = - 0.6

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

x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

Combine all the solutions

x = arccos (0.6) + 2 πn, x = 2 π - arccos (0.6) + 2 πn, x = arccos (- 0.6) + 2 πn, x = - arccos (- 0.6) + 2 πn

Show solutions in decimal form

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

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