QuestionThe smallest positive co-terminal angle for $55^{\circ}$ is

Studdy Solution

STEP 1

Assumptions1. The given angle is $55^{\circ}$ . We are looking for the smallest positive co-terminal angle to this given angle3. Co-terminal angles are angles that share the same initial and terminal sides. They can be found by adding or subtracting multiples of $360^{\circ}$ to the given angle.

STEP 2

First, we need to understand that co-terminal angles can be found by adding or subtracting multiples of $360^{\circ}$ to the given angle. $Co-terminal\, angle = Given\, angle + n \times360^{\circ}$ where n is an integer.

STEP 3

Since we are looking for the smallest positive co-terminal angle, we need to find a value for n such that the result is a positive angle less than $360^{\circ}$ .

STEP 4

Given that the angle is $55^{\circ}$ , we can see that subtracting $360^{\circ}$ would result in a negative angle, and adding $360^{\circ}$ would result in an angle greater than $360^{\circ}$ .

STEP 5

Therefore, the smallest positive co-terminal angle to $55^{\circ}$ is $55^{\circ}$ itself.The smallest positive co-terminal angle to $55^{\circ}$ is $55^{\circ}$ .

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