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Popular Trigonometry >

4sec(θ)+6=-2,0<= θ<2pi

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Solution

4sec(θ)+6=−2,0≤θ<2π

Solution

θ=32π​,θ=34π​
+1
Degrees
θ=120∘,θ=240∘
Solution steps
4sec(θ)+6=−2,0≤θ<2π
Move 6to the right side
4sec(θ)+6=−2
Subtract 6 from both sides4sec(θ)+6−6=−2−6
Simplify4sec(θ)=−8
4sec(θ)=−8
Divide both sides by 4
4sec(θ)=−8
Divide both sides by 444sec(θ)​=4−8​
Simplify
44sec(θ)​=4−8​
Simplify 44sec(θ)​:sec(θ)
44sec(θ)​
Divide the numbers: 44​=1=sec(θ)
Simplify 4−8​:−2
4−8​
Apply the fraction rule: b−a​=−ba​=−48​
Divide the numbers: 48​=2=−2
sec(θ)=−2
sec(θ)=−2
sec(θ)=−2
General solutions for sec(θ)=−2
sec(x) periodicity table with 2πn cycle:
x06π​4π​3π​2π​32π​43π​65π​​sec(x)1323​​2​2Undefined−2−2​−323​​​xπ67π​45π​34π​23π​35π​47π​611π​​sec(x)−1−323​​−2​−2Undefined22​323​​​​
θ=32π​+2πn,θ=34π​+2πn
θ=32π​+2πn,θ=34π​+2πn
Solutions for the range 0≤θ<2πθ=32π​,θ=34π​

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Popular Examples

sqrt(2)sin^2(x)-sin(x)=0cos(2x)=-0.350=3sin(x+pi/2)-cos(t)=cos(t)sin^2(x)-cos(2x)=-1/4

Frequently Asked Questions (FAQ)

  • What is the general solution for 4sec(θ)+6=-2,0<= θ<2pi ?

    The general solution for 4sec(θ)+6=-2,0<= θ<2pi is θ=(2pi)/3 ,θ=(4pi)/3
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