What is the general solution for (10710*cos(2*a))+336.22=0 ?

The general solution for (10710*cos(2*a))+336.22=0 is a=(1.60219…)/2+pin,a=-(1.60219…)/2+pin

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Popular >

(10710cos(2a))+336.22=0

Solution

(10710 \cdot cos (2 \cdot a)) + 336.22 = 0

Solution

a = \frac{1.60219 \dots}{2} + πn, a = - \frac{1.60219 \dots}{2} + πn

Degrees

a = 45.89949 \dots^{\circ} + 18 0^{\circ} n, a = - 45.89949 \dots^{\circ} + 18 0^{\circ} n

Solution steps

(10710 cos (2 a)) + 336.22 = 0

Move

336.22

to the right side

10710 cos (2 a) + 336.22 = 0

Subtract

336.22

from both sides

10710 cos (2 a) + 336.22 - 336.22 = 0 - 336.22

Simplify

10710 cos (2 a) = - 336.22

10710 cos (2 a) = - 336.22

Divide both sides by

10710

10710 cos (2 a) = - 336.22

Divide both sides by

10710

\frac{10710 cos ( 2 a )}{10710} = \frac{- 336.22}{10710}

Simplify

\frac{10710 cos ( 2 a )}{10710} = \frac{- 336.22}{10710}

Simplify

\frac{10710 cos ( 2 a )}{10710} : cos (2 a)

\frac{10710 cos ( 2 a )}{10710}

Divide the numbers:

\frac{10710}{10710} = 1

= cos (2 a)

Simplify

\frac{- 336.22}{10710} : - 0.03139 \dots

\frac{- 336.22}{10710}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{336.22}{10710}

Divide the numbers:

\frac{336.22}{10710} = 0.03139 \dots

= - 0.03139 \dots

cos (2 a) = - 0.03139 \dots

cos (2 a) = - 0.03139 \dots

cos (2 a) = - 0.03139 \dots

Apply trig inverse properties

cos (2 a) = - 0.03139 \dots

General solutions for

cos (2 a) = - 0.03139 \dots

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

2 a = arccos (- 0.03139 \dots) + 2 πn, 2 a = - arccos (- 0.03139 \dots) + 2 πn

2 a = arccos (- 0.03139 \dots) + 2 πn, 2 a = - arccos (- 0.03139 \dots) + 2 πn

Solve

2 a = arccos (- 0.03139 \dots) + 2 πn : a = \frac{arccos ( - 0.03139 \dots )}{2} + πn

2 a = arccos (- 0.03139 \dots) + 2 πn

Divide both sides by

2

2 a = arccos (- 0.03139 \dots) + 2 πn

Divide both sides by

2

\frac{2 a}{2} = \frac{arccos ( - 0.03139 \dots )}{2} + \frac{2 πn}{2}

Simplify

a = \frac{arccos ( - 0.03139 \dots )}{2} + πn

a = \frac{arccos ( - 0.03139 \dots )}{2} + πn

Solve

2 a = - arccos (- 0.03139 \dots) + 2 πn : a = - \frac{arccos ( - 0.03139 \dots )}{2} + πn

2 a = - arccos (- 0.03139 \dots) + 2 πn

Divide both sides by

2

2 a = - arccos (- 0.03139 \dots) + 2 πn

Divide both sides by

2

\frac{2 a}{2} = - \frac{arccos ( - 0.03139 \dots )}{2} + \frac{2 πn}{2}

Simplify

a = - \frac{arccos ( - 0.03139 \dots )}{2} + πn

a = - \frac{arccos ( - 0.03139 \dots )}{2} + πn

a = \frac{arccos ( - 0.03139 \dots )}{2} + πn, a = - \frac{arccos ( - 0.03139 \dots )}{2} + πn

Show solutions in decimal form

a = \frac{1.60219 \dots}{2} + πn, a = - \frac{1.60219 \dots}{2} + πn

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Frequently Asked Questions (FAQ)

What is the general solution for (10710*cos(2*a))+336.22=0 ?
The general solution for (10710*cos(2*a))+336.22=0 is a=(1.60219…)/2+pin,a=-(1.60219…)/2+pin