What is the general solution for 3cos((pix)/(12))+8.4=7 ?

The general solution for 3cos((pix)/(12))+8.4=7 is x=(12*2.05631…)/pi+24n,x=-(12*2.05631…)/pi+24n

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3cos((pix)/(12))+8.4=7

3 cos (\frac{π x}{12}) + 8.4 = 7

x = \frac{12 \cdot 2.05631 \dots}{π} + 24 n, x = - \frac{12 \cdot 2.05631 \dots}{π} + 24 n

Solution steps

3 cos (\frac{π x}{12}) + 8.4 = 7

Move

8.4

to the right side

3 cos (\frac{π x}{12}) = - 1.4

Divide both sides by

3

cos (\frac{π x}{12}) = - 0.46666 \dots

Apply trig inverse properties

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn, \frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn

Solve

\frac{π x}{12} = arccos (- 0.46666 \dots) + 2 πn : x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

Solve

\frac{π x}{12} = - arccos (- 0.46666 \dots) + 2 πn : x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

x = \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n, x = - \frac{12 arccos ( - 0.46666 \dots )}{π} + 24 n

Show solutions in decimal form

x = \frac{12 \cdot 2.05631 \dots}{π} + 24 n, x = - \frac{12 \cdot 2.05631 \dots}{π} + 24 n

sin (x) = \frac{1}{6}, tan (x)

2 sin^{2} (x) + sin (x) - 2 = 0

cos (θ) = \frac{25}{714}

cot^{2} (a) = 1

3 sec^{2} (x) - 4 = 0, 0 \leq x < 2 π

What is the general solution for 3cos((pix)/(12))+8.4=7 ?
The general solution for 3cos((pix)/(12))+8.4=7 is x=(12*2.05631…)/pi+24n,x=-(12*2.05631…)/pi+24n