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4 votes
Cos(θ) − tan(θ)cos(θ) = 0

User StefanJM
by
5.0k points

1 Answer

4 votes

Answer:

θ = 45° and θ = 225°.

Explanation:

cos(θ) − tan(θ)cos(θ) = 0.

Solving for θ:

Since tan(θ) = sin(θ)/cos(θ), therefore:

cos(θ) - cos(θ)*sin(θ)/cos(θ) = 0.

cos(θ) and cos(θ) cancel out so:

cos(θ) - sin(θ) = 0.

cos(θ) = sin(θ).

sin(θ)/cos(θ) = 1

tan(θ) = 1.

Replace θ by the basic angle c.

tan(c) = 1.

c = tan⁻¹(1).

c = 45° (or π/4 radians).

We know that tangent ratio is positive in the first quadrant and the third quadrant. Therefore:

θ = 0° + c° and θ = 180° + c°

θ = 0° + 45° and θ = 180° + 45°

θ = 45° and θ = 225°

In the range [0°, 360°], there lie two answers!!!

User Darkryder
by
5.3k points
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