What is the general solution for cos(x)=0.85 ?

The general solution for cos(x)=0.85 is x=0.55481…+2pin,x=2pi-0.55481…+2pin

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cos(x)=0.85

cos (x) = 0.85

x = 0.55481 \dots + 2 πn, x = 2 π - 0.55481 \dots + 2 πn

Solution steps

cos (x) = 0.85

Apply trig inverse properties

x = arccos (0.85) + 2 πn, x = 2 π - arccos (0.85) + 2 πn

Show solutions in decimal form

x = 0.55481 \dots + 2 πn, x = 2 π - 0.55481 \dots + 2 πn

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

4 = 2 + 2 sin (θ)

2 sin^{2} (x) - 3 sin (x) - 1 = 0

2 sin (6 x) - 1 = 0

sin^{2} (x) = \frac{( 6 m - 5 )}{5}

What is the general solution for cos(x)=0.85 ?
The general solution for cos(x)=0.85 is x=0.55481…+2pin,x=2pi-0.55481…+2pin