What is the general solution for 5+3cos(1/2 x)=7 ?

The general solution for 5+3cos(1/2 x)=7 is x=2*0.84106…+4pin,x=4pi-2*0.84106…+4pin

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5+3cos(1/2 x)=7

5 + 3 cos (\frac{1}{2} x) = 7

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

Solution steps

5 + 3 cos (\frac{1}{2} x) = 7

Move

5

to the right side

3 cos (\frac{1}{2} x) = 2

Divide both sides by

3

cos (\frac{1}{2} x) = \frac{2}{3}

Apply trig inverse properties

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn, \frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

\frac{1}{2} x = arccos (\frac{2}{3}) + 2 πn : x = 2 arccos (\frac{2}{3}) + 4 πn

Solve

\frac{1}{2} x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

x = 2 arccos (\frac{2}{3}) + 4 πn, x = 4 π - 2 arccos (\frac{2}{3}) + 4 πn

Show solutions in decimal form

x = 2 \cdot 0.84106 \dots + 4 πn, x = 4 π - 2 \cdot 0.84106 \dots + 4 πn

cos^{2} (x) sin (x) = sin (x)

sin (2 x - 0.35) = cos (3 x)

2 cos^{2} (x) - 15 cos (x) + 7 = 0

sec (θ) = - \frac{5}{4}

sin^{2} (x) - 4 sin (x) + 1 = 0

What is the general solution for 5+3cos(1/2 x)=7 ?
The general solution for 5+3cos(1/2 x)=7 is x=2*0.84106…+4pin,x=4pi-2*0.84106…+4pin