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

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

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3cos(x)+5=7

3 cos (x) + 5 = 7

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

Degrees

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) + 5 = 7

Move

5

to the right side

3 cos (x) + 5 = 7

Subtract

5

from both sides

3 cos (x) + 5 - 5 = 7 - 5

Simplify

3 cos (x) = 2

3 cos (x) = 2

Divide both sides by

3

3 cos (x) = 2

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

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

3 cos^{2} (x) + 6 cos (x) = - 3

sin (2 x + 4) = cos (4 6^{\circ})

52 cos (x) - 10 sin (x) cos (x) = 0

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

cos^{2} (x) = \frac{( 8 k - 7 )}{7}

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