What is the general solution for cos(x)= 100/130 ?

The general solution for cos(x)= 100/130 is x=0.69315…+2pin,x=2pi-0.69315…+2pin

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cos(x)= 100/130

cos (x) = \frac{100}{130}

x = 0.69315 \dots + 2 πn, x = 2 π - 0.69315 \dots + 2 πn

Solution steps

cos (x) = \frac{100}{130}

Cancel the common factor:

10

cos (x) = \frac{10}{13}

Apply trig inverse properties

x = arccos (\frac{10}{13}) + 2 πn, x = 2 π - arccos (\frac{10}{13}) + 2 πn

Show solutions in decimal form

x = 0.69315 \dots + 2 πn, x = 2 π - 0.69315 \dots + 2 πn

sec^{2} (θ) - 1 = 0, 0 \leq θ \leq 2 π

2 cos^{2} (θ) - 3 cos (θ) = 0, \frac{3 π}{2} < θ < 2 π

cos (θ) = \frac{9}{17}

- 1 = \frac{tan ( x ) - ( \frac{3}{4} )}{1 + tan ( x ) ( \frac{3}{4} )}

cos (x) = - \frac{15}{13}

What is the general solution for cos(x)= 100/130 ?
The general solution for cos(x)= 100/130 is x=0.69315…+2pin,x=2pi-0.69315…+2pin