What is the general solution for 42-25cos(x)=31 ?

The general solution for 42-25cos(x)=31 is x=1.11519…+2pin,x=2pi-1.11519…+2pin

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42-25cos(x)=31

42 - 25 cos (x) = 31

x = 1.11519 \dots + 2 πn, x = 2 π - 1.11519 \dots + 2 πn

Degrees

x = 63.89611 \dots^{\circ} + 36 0^{\circ} n, x = 296.10388 \dots^{\circ} + 36 0^{\circ} n

Solution steps

42 - 25 cos (x) = 31

Move

42

to the right side

42 - 25 cos (x) = 31

Subtract

42

from both sides

42 - 25 cos (x) - 42 = 31 - 42

Simplify

- 25 cos (x) = - 11

- 25 cos (x) = - 11

Divide both sides by

- 25

- 25 cos (x) = - 11

Divide both sides by

- 25

\frac{- 25 cos ( x )}{- 25} = \frac{- 11}{- 25}

Simplify

cos (x) = \frac{11}{25}

cos (x) = \frac{11}{25}

Apply trig inverse properties

cos (x) = \frac{11}{25}

General solutions for

cos (x) = \frac{11}{25}

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

x = arccos (\frac{11}{25}) + 2 πn, x = 2 π - arccos (\frac{11}{25}) + 2 πn

x = arccos (\frac{11}{25}) + 2 πn, x = 2 π - arccos (\frac{11}{25}) + 2 πn

Show solutions in decimal form

x = 1.11519 \dots + 2 πn, x = 2 π - 1.11519 \dots + 2 πn

2 sec^{2} (x) = 5 tan (x)

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

sin (- t) = \frac{3}{10}

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

c, e = r (sec (\frac{c}{2}) - 1)

What is the general solution for 42-25cos(x)=31 ?
The general solution for 42-25cos(x)=31 is x=1.11519…+2pin,x=2pi-1.11519…+2pin