Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
tan θ = −square root of 3
answer in radian and please use the k integer
your calculator should do this easily. You are looking for act tan function, or INV tan function.
3
sqrt
+-
invTan key (make certain the calc is in rad mode on angles)
Do you have your calculator book?
To solve the equation tan θ = -√3, we first need to find the reference angle.
Reference angle is the positive acute angle formed between the terminal side of an angle and the x-axis.
Given that tan θ = -√3, we can determine the reference angle using the ratio of the sides of a right triangle. Since the tangent is negative, we know that θ is in either the second or fourth quadrant.
In the second quadrant, the reference angle θ' would have the same tangent value, which is √3 (since tan is positive in the second quadrant). This means that tan θ' = √3.
Using the inverse tangent function (arctan) on both sides, we get θ' = arctan(√3).
To find the angle in the fourth quadrant, we add π (180°) to the reference angle: θ = π + θ'.
Now we can calculate the values of θ in radians, using the formula θ = π + θ' + kπ, where k is any integer.
θ = π + arctan(√3) + kπ
Substituting the value of arctan(√3) as approximately 1.04 radians, we get:
θ = π + 1.04 + kπ (rounded to two decimal places)
Therefore, the solutions for the given equation are:
θ ≈ π + 1.04 + kπ, where k is any integer.