What is the general solution for 4cos(x+pi/4)=-1 ?

The general solution for 4cos(x+pi/4)=-1 is x=1.82347…+2pin-pi/4 ,x=-1.82347…+2pin-pi/4

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4cos(x+pi/4)=-1

4 cos (x + \frac{π}{4}) = - 1

x = 1.82347 \dots + 2 πn - \frac{π}{4}, x = - 1.82347 \dots + 2 πn - \frac{π}{4}

Solution steps

4 cos (x + \frac{π}{4}) = - 1

Divide both sides by

4

cos (x + \frac{π}{4}) = - \frac{1}{4}

Apply trig inverse properties

x + \frac{π}{4} = arccos (- \frac{1}{4}) + 2 πn, x + \frac{π}{4} = - arccos (- \frac{1}{4}) + 2 πn

Solve

x + \frac{π}{4} = arccos (- \frac{1}{4}) + 2 πn : x = arccos (- \frac{1}{4}) + 2 πn - \frac{π}{4}

Solve

x + \frac{π}{4} = - arccos (- \frac{1}{4}) + 2 πn : x = - arccos (- \frac{1}{4}) + 2 πn - \frac{π}{4}

x = arccos (- \frac{1}{4}) + 2 πn - \frac{π}{4}, x = - arccos (- \frac{1}{4}) + 2 πn - \frac{π}{4}

Show solutions in decimal form

x = 1.82347 \dots + 2 πn - \frac{π}{4}, x = - 1.82347 \dots + 2 πn - \frac{π}{4}

cos (x) = \frac{3}{25}

csc (θ) + 3.35 = 0

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

y, 5^{2 x} - sin (y) = x

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

What is the general solution for 4cos(x+pi/4)=-1 ?
The general solution for 4cos(x+pi/4)=-1 is x=1.82347…+2pin-pi/4 ,x=-1.82347…+2pin-pi/4