tan theta= square root of 3 / 3 if o degrees is less than or equal to theta less than o equal to 360
tan Ø = √3/3 0 ≤ Ø ≤ 360°
are we solving for Ø ??
Ø must be in I or III
the angle in standard position is 30°
so Ø = 30° or Ø = 210°
To find the value of theta given that tan(theta) = √3/3 and 0° ≤ theta < 360°, we can use the inverse tangent function (also known as arctan). The inverse tangent function can be denoted as atan or tan^(-1).
First, let's take the inverse tangent of both sides of the equation:
arctan(tan(theta)) = arctan(√3/3)
Since arctan(tan(theta)) simplifies to theta, we have:
theta = arctan(√3/3)
Now, we need to evaluate the inverse tangent of (√3/3). In order to find the angle in the given range (0° ≤ theta < 360°), we need to consider the quadrant in which the angle lies.
Since the value of (√3/3) is positive, we know that the angle lies in either the first quadrant (0° < theta < 90°) or in the third quadrant (180° < theta < 270°). We can check for both possibilities.
Using a calculator or a trigonometric table, we find:
For the first quadrant (0° < theta < 90°):
theta = arctan(√3/3) ≈ 30°
For the third quadrant (180° < theta < 270°):
theta = arctan(√3/3) + 180° ≈ 210°
So, the two possible solutions for theta are 30° and 210°.