What is the general solution for 4cos(x+70)=3 ?

The general solution for 4cos(x+70)=3 is x=0.72273…+360n-70,x=360-0.72273…+360n-70

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4cos(x+70)=3

4 cos (x + 7 0^{\circ}) = 3

x = 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}

Radians

x = 0.72273 \dots - \frac{7 π}{18} + 2 πn, x = 2 π - 0.72273 \dots - \frac{7 π}{18} + 2 πn

Solution steps

4 cos (x + 7 0^{\circ}) = 3

Divide both sides by

4

4 cos (x + 7 0^{\circ}) = 3

Divide both sides by

4

\frac{4 cos ( x + 7 0 ^{\circ} )}{4} = \frac{3}{4}

Simplify

cos (x + 7 0^{\circ}) = \frac{3}{4}

cos (x + 7 0^{\circ}) = \frac{3}{4}

Apply trig inverse properties

cos (x + 7 0^{\circ}) = \frac{3}{4}

General solutions for

cos (x + 7 0^{\circ}) = \frac{3}{4}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Solve

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n : x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Move

7 0^{\circ}

to the right side

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Subtract

7 0^{\circ}

from both sides

x + 7 0^{\circ} - 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

Simplify

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

Solve

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Move

7 0^{\circ}

to the right side

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Subtract

7 0^{\circ}

from both sides

x + 7 0^{\circ} - 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

Show solutions in decimal form

x = 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}

4 cos (2 x) = 0

tan (3 x) = - \frac{3}{3}

tan^{2} (x) + 3 = 2 sec^{2} (x)

8 sin^{2} (θ) - 2 = 0

4 sin (2 x) sin (x) = 4 cos (x)

What is the general solution for 4cos(x+70)=3 ?
The general solution for 4cos(x+70)=3 is x=0.72273…+360n-70,x=360-0.72273…+360n-70