What is the general solution for cos(x)=(2.16)/(3.42) ?

The general solution for cos(x)=(2.16)/(3.42) is x=0.88720…+2pin,x=2pi-0.88720…+2pin

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cos(x)=(2.16)/(3.42)

cos (x) = \frac{2.16}{3.42}

x = 0.88720 \dots + 2 πn, x = 2 π - 0.88720 \dots + 2 πn

Solution steps

cos (x) = \frac{2.16}{3.42}

Apply trig inverse properties

x = arccos (\frac{2.16}{3.42}) + 2 πn, x = 2 π - arccos (\frac{2.16}{3.42}) + 2 πn

Show solutions in decimal form

x = 0.88720 \dots + 2 πn, x = 2 π - 0.88720 \dots + 2 πn

2 cos^{2} (θ) - 3 sin (θ) - 3 = 0

sinh (x) = \frac{5}{12}, cosh (x)

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

cos^{4} (x) = 1 + sin^{4} (x)

- 4 cos^{2} (θ) - 11 cos (θ) - 1 = - 7 cos (θ)

What is the general solution for cos(x)=(2.16)/(3.42) ?
The general solution for cos(x)=(2.16)/(3.42) is x=0.88720…+2pin,x=2pi-0.88720…+2pin