What is the general solution for 7-5cos(x)=10 ?

The general solution for 7-5cos(x)=10 is x=2.21429…+2pin,x=-2.21429…+2pin

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7-5cos(x)=10

7 - 5 cos (x) = 10

x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

Degrees

x = 126.86989 \dots^{\circ} + 36 0^{\circ} n, x = - 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

7 - 5 cos (x) = 10

Move

7

to the right side

7 - 5 cos (x) = 10

Subtract

7

from both sides

7 - 5 cos (x) - 7 = 10 - 7

Simplify

- 5 cos (x) = 3

- 5 cos (x) = 3

Divide both sides by

- 5

- 5 cos (x) = 3

Divide both sides by

- 5

\frac{- 5 cos ( x )}{- 5} = \frac{3}{- 5}

Simplify

cos (x) = - \frac{3}{5}

cos (x) = - \frac{3}{5}

Apply trig inverse properties

cos (x) = - \frac{3}{5}

General solutions for

cos (x) = - \frac{3}{5}

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

x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

Show solutions in decimal form

x = 2.21429 \dots + 2 πn, x = - 2.21429 \dots + 2 πn

sin^{2} (θ) - 2 = sin (θ)

5 + 4 cos (x) = 0

csc^{2} (x) - csc (x) - 2 = 0, 0 \leq x \leq 2 π

sinh (x - 1) = 0

32 cos (x) - 6 sin (x) cos (x) = 0

What is the general solution for 7-5cos(x)=10 ?
The general solution for 7-5cos(x)=10 is x=2.21429…+2pin,x=-2.21429…+2pin