What is the general solution for cos(x)=0.65 ?

The general solution for cos(x)=0.65 is x=0.86321…+2pin,x=2pi-0.86321…+2pin

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cos(x)=0.65

cos (x) = 0.65

x = 0.86321 \dots + 2 πn, x = 2 π - 0.86321 \dots + 2 πn

Solution steps

cos (x) = 0.65

Apply trig inverse properties

x = arccos (0.65) + 2 πn, x = 2 π - arccos (0.65) + 2 πn

Show solutions in decimal form

x = 0.86321 \dots + 2 πn, x = 2 π - 0.86321 \dots + 2 πn

- 2 sin (\frac{x}{2}) - 1 = - 2 cos (\frac{x}{2}) - 1

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

tan (θ) = 30.48 (80)

cos (x) = a, \frac{3 π}{2} \leq x \leq 2 π

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

What is the general solution for cos(x)=0.65 ?
The general solution for cos(x)=0.65 is x=0.86321…+2pin,x=2pi-0.86321…+2pin