What is the general solution for cos(x)= 10/15 ?

The general solution for cos(x)= 10/15 is x=0.84106…+2pin,x=2pi-0.84106…+2pin

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cos(x)= 10/15

cos (x) = \frac{10}{15}

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Degrees

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x) = \frac{10}{15}

Cancel the common factor:

5

cos (x) = \frac{2}{3}

Apply trig inverse properties

cos (x) = \frac{2}{3}

General solutions for

cos (x) = \frac{2}{3}

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

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

\frac{sin ( b )}{350} = \frac{sin ( 15 3 ^{\circ} )}{536}

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

2 cos (2 x) + cos (x) = 0

sin (x) = - 0.435

sin (θ) = \frac{10 sin ( 10 5 ^{\circ} )}{24.6}

What is the general solution for cos(x)= 10/15 ?
The general solution for cos(x)= 10/15 is x=0.84106…+2pin,x=2pi-0.84106…+2pin