Final answer:
To find arctan(-√3/3), we need to find the angle whose tangent is -√3/3. By setting up a right triangle and using the Pythagorean theorem, we can find the length of the hypotenuse to be 2√3. Then, using the fact that the tangent of an angle is equal to the opposite side divided by the adjacent side, we can find the angle to be approximately -30.96°.
Step-by-step explanation:
To find arctan(-√3/3), we need to find the angle whose tangent is -√3/3. The tangent function is the ratio of the opposite side to the adjacent side of a right triangle. Since -√3/3 is negative, the angle must be in Quadrant IV. In this quadrant, the tangent value is negative, so we can ignore the negative sign.
We can set up a right triangle with the opposite side as -√3 and the adjacent side as 3. Using the Pythagorean theorem, we can find the length of the hypotenuse to be 2:
a² + b² = c²
3² + (-√3)² = c²
9 + 3 = c²
c = √(12) = 2√3
Therefore, the angle is arctan(-√3/3) = arctan(-√3/3) = ?
To find the angle, we can use the fact that the tangent of an angle is equal to the opposite side divided by the adjacent side:
tan(?) = (-√3/3) = -1/√3
We can now apply the arctan function to both sides of the equation:
? = arctan(-1/√3)
Using a calculator or reference table, we find that arctan(-1/√3) is approximately -30.96°.