Question

How to find the two coterminal angles (one positive and one negative) for angle $ - 36^\circ $.

Answer 1

Hint:Coterminal Angles are angles who share the identical initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to every angle, counting on whether the given angle is in degrees or radians.For example, the angles 30°, –330° and 390° are all coterminal.

Complete step by step answer:
We know that coterminal angles are those who share the same initial and terminal sides. The formula for finding the coterminal angles of a given angle “x” is \[(x + 360n)^\circ \], where n is any integer.
In the question we have $x = - 36^\circ $. Putting the value in the formula, we get \[( - 36 + 360n)^\circ \].
For $n = 1$, \[( - 36 + (360 \times 1))^\circ = 324^\circ \](one positive angle)
For $n = 2$, \[( - 36 + (360 \times - 1))^\circ = - 396^\circ \](one negative angle)

Hence, the two coterminal angles (one positive and one negative) for angle $ - 36^\circ $ are $324^\circ$ and $- 396^\circ$.

Additional information:
The reference angle is the oblique angle (the smallest angle) formed by the terminal side of the given angle and also the x-axis. Reference angles may appear in all told four quadrants. Angles in quadrant I are their own reference angles. If two angles in standard position have the identical terminal side, they're called coterminal angles.

Note:Angles are classified as follows based on their position, Standard Position of an Angle - Initial Side - Terminal Side. An angle is in standard position within the coordinate plane if its vertex is found at the origin and one ray is on the positive x-axis. The ray on the x-axis is termed the initial side and therefore the other ray is termed the terminal side.