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

Tan theta -1=0

Write your answer in radians in terms of pi

Find all solutions of the equation in the interval 02pi Tan theta 10 Write your answer in radians in terms of pi class=

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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}.

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}

Learn more about trigonometric ratios here:

https://brainly.com/question/8120556

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