What is the general solution for 4cos(x-45)+7=10 ?

The general solution for 4cos(x-45)+7=10 is x=0.72273…+360n+45,x=360-0.72273…+360n+45

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Popular >

4cos(x-45)+7=10

Solution

4 cos (x - 4 5^{\circ}) + 7 = 10

Solution

x = 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}

Radians

x = 0.72273 \dots + \frac{π}{4} + 2 πn, x = 2 π - 0.72273 \dots + \frac{π}{4} + 2 πn

Solution steps

4 cos (x - 4 5^{\circ}) + 7 = 10

Move

7

to the right side

4 cos (x - 4 5^{\circ}) + 7 = 10

Subtract

7

from both sides

4 cos (x - 4 5^{\circ}) + 7 - 7 = 10 - 7

Simplify

4 cos (x - 4 5^{\circ}) = 3

4 cos (x - 4 5^{\circ}) = 3

Divide both sides by

4

4 cos (x - 4 5^{\circ}) = 3

Divide both sides by

4

\frac{4 cos ( x - 4 5 ^{\circ} )}{4} = \frac{3}{4}

Simplify

cos (x - 4 5^{\circ}) = \frac{3}{4}

cos (x - 4 5^{\circ}) = \frac{3}{4}

Apply trig inverse properties

cos (x - 4 5^{\circ}) = \frac{3}{4}

General solutions for

cos (x - 4 5^{\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 - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Solve

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n : x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Move

4 5^{\circ}

to the right side

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Add

4 5^{\circ}

to both sides

x - 4 5^{\circ} + 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Solve

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Move

4 5^{\circ}

to the right side

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Add

4 5^{\circ}

to both sides

x - 4 5^{\circ} + 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Show solutions in decimal form

x = 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}

Popular Examples

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

-2=2cos(3θ)

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cos(x)= 4/30

cos (x) = \frac{4}{30}

solvefor t,x=sin(2t)+1 solve for

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cos(x)= 4/35

cos (x) = \frac{4}{35}

Frequently Asked Questions (FAQ)

What is the general solution for 4cos(x-45)+7=10 ?
The general solution for 4cos(x-45)+7=10 is x=0.72273…+360n+45,x=360-0.72273…+360n+45