What is the general solution for 31.91cos(x)=20.48 ?

The general solution for 31.91cos(x)=20.48 is x=0.87394…+2pin,x=2pi-0.87394…+2pin

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31.91cos(x)=20.48

31.91 cos (x) = 20.48

x = 0.87394 \dots + 2 πn, x = 2 π - 0.87394 \dots + 2 πn

Degrees

x = 50.07344 \dots^{\circ} + 36 0^{\circ} n, x = 309.92655 \dots^{\circ} + 36 0^{\circ} n

Solution steps

31.91 cos (x) = 20.48

Multiply both sides by

100

31.91 cos (x) = 20.48

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

31.91 cos (x) \cdot 100 = 20.48 \cdot 100

Refine

3191 cos (x) = 2048

3191 cos (x) = 2048

Divide both sides by

3191

3191 cos (x) = 2048

Divide both sides by

3191

\frac{3191 cos ( x )}{3191} = \frac{2048}{3191}

Simplify

cos (x) = \frac{2048}{3191}

cos (x) = \frac{2048}{3191}

Apply trig inverse properties

cos (x) = \frac{2048}{3191}

General solutions for

cos (x) = \frac{2048}{3191}

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

x = arccos (\frac{2048}{3191}) + 2 πn, x = 2 π - arccos (\frac{2048}{3191}) + 2 πn

x = arccos (\frac{2048}{3191}) + 2 πn, x = 2 π - arccos (\frac{2048}{3191}) + 2 πn

Show solutions in decimal form

x = 0.87394 \dots + 2 πn, x = 2 π - 0.87394 \dots + 2 πn

7 sin (x) + 7 sin (x) tan (x) = 0

0 = cos (20 t) - cos (20.02 t)

2 tan (2 x - 10) = 3.4641

12 cos (\frac{π}{3} x) + 8 = 0

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

What is the general solution for 31.91cos(x)=20.48 ?
The general solution for 31.91cos(x)=20.48 is x=0.87394…+2pin,x=2pi-0.87394…+2pin