Question

Find all solutions of the equation in the interval [0,2pi)

Tan theta -1=0

Write your answer in radians in terms of pi

Answer 1

Answer:

{π/4, 5π/4}

Step-by-step explanation:

Tan theta -1=0 could be rewritten as tan Ф = 1.  The tangent function is 1 at Ф = π/4.  As the period of the tangent function is π,

tan Ф = 1 will be true for Ф = π/4 + π, or (5/4)π.

The solution set is {π/4, 5π/4}.

Answer 2

The solutions of the given equation are -1, 0, -2, 0, -2 for the values of θ in the interval [0, 2π) respectively.

How the tangent ratio (tan) is defined?

A tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.

tan θ = (sin θ)/(cos θ)

Solving the given equation:

The given equation is

tan θ - 1 =0

solving for the values in between [0, 2π)

In this interval, the possible values for θ(in the case of tan) are 0, π/4, 3π/4, 5π/4, and 7π/4.

So, the solutions are:

for θ = 0,

⇒ tan (0) - 1 = -1

for θ = π/4,

⇒ tan(π/4) - 1 = 0

for θ = 3π/4,

⇒ tan(3π/4) - 1 = -2

for θ = 5π/4,

⇒ tan(5π/4) - 1 = 0

for θ = 7π/4,

⇒ tan(7π/4) - 1 = -2

Thus, the solution set for the given equation in the interval [0, 2π) is {-1, 0, -2, 0, -2}

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