What is the general solution for 391=78*21.5*cos(x) ?

The general solution for 391=78*21.5*cos(x) is x=1.33547…+2pin,x=2pi-1.33547…+2pin

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391=7821.5cos(x)

391 = 78 \cdot 21.5 \cdot cos (x)

x = 1.33547 \dots + 2 πn, x = 2 π - 1.33547 \dots + 2 πn

Degrees

x = 76.51714 \dots^{\circ} + 36 0^{\circ} n, x = 283.48285 \dots^{\circ} + 36 0^{\circ} n

Solution steps

391 = 78 \cdot 21.5 cos (x)

Switch sides

78 \cdot 21.5 cos (x) = 391

Divide both sides by

1677

78 \cdot 21.5 cos (x) = 391

Divide both sides by

1677

\frac{78 \cdot 21.5 cos ( x )}{1677} = \frac{391}{1677}

Simplify

cos (x) = \frac{391}{1677}

cos (x) = \frac{391}{1677}

Apply trig inverse properties

cos (x) = \frac{391}{1677}

General solutions for

cos (x) = \frac{391}{1677}

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

x = arccos (\frac{391}{1677}) + 2 πn, x = 2 π - arccos (\frac{391}{1677}) + 2 πn

x = arccos (\frac{391}{1677}) + 2 πn, x = 2 π - arccos (\frac{391}{1677}) + 2 πn

Show solutions in decimal form

x = 1.33547 \dots + 2 πn, x = 2 π - 1.33547 \dots + 2 πn

5 tan (θ) - 9 = - 6 tan (θ) + 8

81 (cos^{2} (x)) = 6

(cos (x) - 2) (cos (x) + 1) = 0

6 cos^{2} (x) + sin (x) - 5 = 0

tan (θ) = \frac{23}{72}

What is the general solution for 391=78*21.5*cos(x) ?
The general solution for 391=78*21.5*cos(x) is x=1.33547…+2pin,x=2pi-1.33547…+2pin