Asked by Gina
Solve each equation for 0<_ 0<_ 2pi(3.14)
a) 2tan^20 = 3tan0 - 1
a) 2tan^20 = 3tan0 - 1
Answers
Answered by
Jai
Let tan(θ) = x
So that,
2tan^2 (θ) = 3tan(θ) - 1
becomes
2x^2 = 3x - 1
Solving,
2x^2 - 3x + 1 = 0
(2x - 1)(x - 1) = 0
2x = 1
x = 1/2 : first root
x = 1 : second root
Substitute back tan(θ):
tan(θ) = 1/2
θ = tan^-1 (1/2)
θ = 26.6 degrees
tan(θ) = 1
θ = tan^-1 (1)
θ = 45 degrees
hope this helps~ `u`
So that,
2tan^2 (θ) = 3tan(θ) - 1
becomes
2x^2 = 3x - 1
Solving,
2x^2 - 3x + 1 = 0
(2x - 1)(x - 1) = 0
2x = 1
x = 1/2 : first root
x = 1 : second root
Substitute back tan(θ):
tan(θ) = 1/2
θ = tan^-1 (1/2)
θ = 26.6 degrees
tan(θ) = 1
θ = tan^-1 (1)
θ = 45 degrees
hope this helps~ `u`
Answered by
Reiny
There are actually 4 solutions,
from Jai's:
tanØ = 1/2
so by the CAST rule, Ø is in either the first or the third quadrant
Ø = 26.6° ---- Jai's answer
Ø = 180+26.6= 206.6°
if tanØ = 1
Ø = 45° , ----- again, Jai's answer
Ø = 180+45 = 225°
in degrees:
Ø = 26.6° , 206.6° , 45° , 225°
Furthermore, since the domain was stated as
0 ≤ Ø ≤ 2π , that is, in radians, we should state our answer in radians
Ø = .46365 , 3.60524 , π/4 , 5π/4
from Jai's:
tanØ = 1/2
so by the CAST rule, Ø is in either the first or the third quadrant
Ø = 26.6° ---- Jai's answer
Ø = 180+26.6= 206.6°
if tanØ = 1
Ø = 45° , ----- again, Jai's answer
Ø = 180+45 = 225°
in degrees:
Ø = 26.6° , 206.6° , 45° , 225°
Furthermore, since the domain was stated as
0 ≤ Ø ≤ 2π , that is, in radians, we should state our answer in radians
Ø = .46365 , 3.60524 , π/4 , 5π/4
Answered by
Gina
thank you! i see where i did my calculations wrong..
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