What is the general solution for 0.2=cos(2pit) ?

The general solution for 0.2=cos(2pit) is t=(1.36943…)/(2pi)+n,t=1-(1.36943…)/(2pi)+n

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0.2=cos(2pit)

0.2 = cos (2 π t)

t = \frac{1.36943 \dots}{2 π} + n, t = 1 - \frac{1.36943 \dots}{2 π} + n

Solution steps

0.2 = cos (2 π t)

Switch sides

cos (2 π t) = 0.2

Apply trig inverse properties

2 π t = arccos (0.2) + 2 πn, 2 π t = 2 π - arccos (0.2) + 2 πn

Solve

2 π t = arccos (0.2) + 2 πn : t = \frac{arccos ( 0.2 )}{2 π} + n

Solve

2 π t = 2 π - arccos (0.2) + 2 πn : t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

t = \frac{arccos ( 0.2 )}{2 π} + n, t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

Show solutions in decimal form

t = \frac{1.36943 \dots}{2 π} + n, t = 1 - \frac{1.36943 \dots}{2 π} + n

4 cos^{2} (2 x) - 1 = 1, 0 \leq x \leq 2 π

sec (\frac{β}{4}) csc (\frac{β}{4}) = 2 csc (\frac{β}{4})

sin (x) = \frac{1}{7}

tan (\frac{θ}{2}) = - 1

tan (\frac{θ}{2}) = 1

What is the general solution for 0.2=cos(2pit) ?
The general solution for 0.2=cos(2pit) is t=(1.36943…)/(2pi)+n,t=1-(1.36943…)/(2pi)+n