What are the values of theta in the interval 0degrees less than or equal to theta less than or equal to 360 degrees that satisfy the equation tan theta - radical3=0
if it is multiple choice you could just plug in the answers for theta and figure out which ones equal 0
so just
tan Ø = √3
by CAST rule, the tangent is positive in I and III
so Ø = 60° or Ø = 240°
To find the values of theta that satisfy the equation tan(theta) - √3 = 0, we can follow these steps:
Step 1: Use the fact that tan(theta) = √3 to find the possible solutions.
By definition, tan(theta) = opposite/adjacent = √3/1.
In a right-angled triangle, this means that the length of the side opposite theta is √3, and the length of the adjacent side is 1. This triangle can be visualized as an equilateral triangle.
Step 2: Determine the corresponding angle values.
To find the values of theta that satisfy tan(theta) = √3, we need to consider the unit circle and the behavior of the tangent function.
In the unit circle, tan(theta) is positive in quadrants I and III. Since we are looking for values of theta in the interval 0 ≤ theta ≤ 360 degrees, this means we need to consider the angles in quadrants I and III.
In quadrant I, the angle whose tangent is equal to √3 is 60 degrees (or π/3 radians).
In quadrant III, the angle whose tangent is equal to √3 is 180 + 60 = 240 degrees (or 4π/3 radians).
Step 3: Finalize the solution set.
The values of theta that satisfy the equation tan(theta) - √3 = 0 in the interval 0 ≤ theta ≤ 360 degrees are 60 degrees and 240 degrees (or π/3 and 4π/3 radians, respectively).
Therefore, the solution set is {60, 240} degrees (or {π/3, 4π/3} radians).