What is the general solution for 16=4+9-12cos(x) ?

The general solution for 16=4+9-12cos(x) is x=1.82347…+2pin,x=-1.82347…+2pin

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16=4+9-12cos(x)

16 = 4 + 9 - 12 cos (x)

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

16 = 4 + 9 - 12 cos (x)

Switch sides

4 + 9 - 12 cos (x) = 16

Add the numbers:

4 + 9 = 13

- 12 cos (x) + 13 = 16

Move

13

to the right side

- 12 cos (x) = 3

Divide both sides by

- 12

cos (x) = - \frac{1}{4}

Apply trig inverse properties

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

Show solutions in decimal form

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

tanh (z) + 2 = 0

cos^{2} (a) = \frac{2}{3 sin ( a )}

5 cos (5 x) = 2

4 sin (x) - sin^{3} (x) - 1 = 0

1 - tan (a) = \frac{- 1}{3}

What is the general solution for 16=4+9-12cos(x) ?
The general solution for 16=4+9-12cos(x) is x=1.82347…+2pin,x=-1.82347…+2pin