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Trig help please!?

0 votes

1. (tan θ − 4)(25 sin2 θ − 1) = 0 

2. 3 tan3θ = tan θ 

asked Jun 17, 2014 in TRIGONOMETRY by anonymous

2 Answers

0 votes

1) The trigonometric equation is (tan θ − 4)(25 sin2 θ − 1) = 0.

Split the equations.

tan θ − 4 = 0 and 25 sin2 θ − 1 = 0

Take tan θ − 4 = 0.

Add 4 to each side.

tan θ − 4 + 4  = 0 + 4

tan θ = 4

Take the inverse tangent of both sides.

θ = tan-1(4) + nπ for n Є Z.

Take 25 sin2θ − 1 = 0.

Add 1 to each side.

25 sin2θ − 1 + 1 = 0 + 1

25 sin2θ = 1

Divide each side by 25.

(25 sin2θ) / 25 = 1/25

sin2θ = 1/25

Take the invere sine of both sides.

2θ = 2πn ± sin-1(1/25) for n Є Z.

2θ = 2πn₁ + sin-1(1/25) n₁ Є Z or 2θ = 2πn₂ + π - sin-1(1/25) n₂ Є Z.

θ = (1/2) {2πn₁ + sin-1(1/25)} n₁ Є Z or θ = (1/2) {2πn₂ + π - sin-1(1/25)} n₂ Є Z.

θ = πn₁ + (1/2)sin-1(1/25) n₁ Є Z or θ = πn₂ + π/2 - (1/2)sin-1(1/25) n₂ Є Z.

The solutions are θ = tan-1(4) + nπ for n Є Z or θ = πn₁ + (1/2)sin-1(1/25) n₁ Є Z or θ = πn₂ + π/2 - (1/2)sin-1(1/25) n₂ Є Z.

 

answered Jun 17, 2014 by joly Scholar
0 votes

2) The equation is 3 tan3θ = tan θ.

Formula for  image.

image

image

Take Least Common Multiple.

image

image

image

image

image

Divide each side by 8.

image

Take inverse tangent of both sides.

image

image

image

The solution is image.

 

answered Jun 17, 2014 by joly Scholar

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