What is the general solution for cos(x)=0.75 ?

The general solution for cos(x)=0.75 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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cos(x)=0.75

cos (x) = 0.75

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Degrees

x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x) = 0.75

Apply trig inverse properties

cos (x) = 0.75

General solutions for

cos (x) = 0.75

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

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

x = arccos (0.75) + 2 πn, x = 2 π - arccos (0.75) + 2 πn

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

cos (x) = 0.76

0 = 4 cos (2 x)

cos (x) + 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

82 cos (θ) + 6 = - 2

cos (- θ) = - cos (θ)

What is the general solution for cos(x)=0.75 ?
The general solution for cos(x)=0.75 is x=0.72273…+2pin,x=2pi-0.72273…+2pin