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Popular Trigonometry >

24=32+8-2*sqrt(32*8)*cos(θ)

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Solution

24=32+8−2⋅32⋅8​⋅cos(θ)

Solution

θ=3π​+2πn,θ=35π​+2πn
+1
Degrees
θ=60∘+360∘n,θ=300∘+360∘n
Solution steps
24=32+8−232⋅8​cos(θ)
Switch sides32+8−232⋅8​cos(θ)=24
232⋅8​cos(θ)=32cos(θ)
232⋅8​cos(θ)
32⋅8​=16
32⋅8​
Multiply the numbers: 32⋅8=256=256​
Factor the number: 256=162=162​
Apply radical rule: 162​=16=16
=2⋅16cos(θ)
Multiply the numbers: 2⋅16=32=32cos(θ)
32+8−32cos(θ)=24
Add the numbers: 32+8=40−32cos(θ)+40=24
Move 40to the right side
−32cos(θ)+40=24
Subtract 40 from both sides−32cos(θ)+40−40=24−40
Simplify−32cos(θ)=−16
−32cos(θ)=−16
Divide both sides by −32
−32cos(θ)=−16
Divide both sides by −32−32−32cos(θ)​=−32−16​
Simplify
−32−32cos(θ)​=−32−16​
Simplify −32−32cos(θ)​:cos(θ)
−32−32cos(θ)​
Apply the fraction rule: −b−a​=ba​=3232cos(θ)​
Divide the numbers: 3232​=1=cos(θ)
Simplify −32−16​:21​
−32−16​
Apply the fraction rule: −b−a​=ba​=3216​
Cancel the common factor: 16=21​
cos(θ)=21​
cos(θ)=21​
cos(θ)=21​
General solutions for cos(θ)=21​
cos(x) periodicity table with 2πn cycle:
x06π​4π​3π​2π​32π​43π​65π​​cos(x)123​​22​​21​0−21​−22​​−23​​​xπ67π​45π​34π​23π​35π​47π​611π​​cos(x)−1−23​​−22​​−21​021​22​​23​​​​
θ=3π​+2πn,θ=35π​+2πn
θ=3π​+2πn,θ=35π​+2πn

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Popular Examples

sin(45+a)cos(45+a)=(sqrt(2))/2sin(z)=sqrt(2)sin(x)= 9/104sin(x)-sec(x)=0sin^2(x)=(1-cos^2(x))/2

Frequently Asked Questions (FAQ)

  • What is the general solution for 24=32+8-2*sqrt(32*8)*cos(θ) ?

    The general solution for 24=32+8-2*sqrt(32*8)*cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin
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