QuestionFind the smallest positive angle (in degrees) coterminal with $A=247^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The given angle A is247 degrees. . We are looking for the least positive angle that is coterminal with A.
3. We understand that two angles are coterminal if they differ by a multiple of360 degrees.

STEP 2

We know that coterminal angles can be found by adding or subtracting multiples of360 degrees to the given angle. Since we are looking for the least positive angle, we should subtract360 degrees from the given angle until we get a positive angle less than360 degrees.
$B = A -360n$ where B is the coterminal angle we are looking for, A is the given angle, and n is the number of times we subtract360 degrees.

STEP 3

Plug in the given value for the angle A into the equation.
$B =247 -360n$

STEP 4

Since247 is less than360, we don't need to subtract360 from it. So, n =0.
$B =247 -360 \\times0$

STEP 5

Calculate the value of B.
$B =247 -0 =247$ The least positive angle that is coterminal with247 degrees is247 degrees itself.

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