Graph tan(theta)=- square root of 3

Problem

tan(θ)=−√(,3)

Solution

1. Identify the equation as a trigonometric equation where we need to find the values of θ that satisfy the given condition.

2. Determine the reference angle by finding the value of θ in the first quadrant where tan(θ)=√(,3)

3. Calculate the reference angle using the known values of the tangent function, which gives (θ_ref)=π/3 or 60

4. Locate the quadrants where the tangent function is negative, which are Quadrant II and Quadrant IV.

5. Find the specific angles in those quadrants using the reference angle.

6. Apply the formula for Quadrant II: θ=π−π/3=(2*π)/3

7. Apply the formula for Quadrant IV: θ=2*π−π/3=(5*π)/3

8. Generalize the solution because the tangent function has a period of π

Final Answer

θ=(2*π)/3+n*π

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