Question

How to draw ${{300}^{\circ }}$ in standard position and find one positive and one negative angle that is coterminal to a given angle.

Answer 1

Hint: To draw an angle in standard position take one arm of angle along x axis and then rotate the angle counterclockwise for positive angle. To find positive coterminal angle add ${{360}^{\circ }}$ to the angle and to find negative coterminal angle subtract ${{360}^{\circ }}$ to the given angle

Complete step-by-step answer:
Now let us first understand angles in standard position.
Angles in standard position means it has one arm along the positive x axis.
Now if we rotate the angle counter clockwise we get a positive angle. If we rotate the angle clockwise we get a negative angle.
For example if we rotate the angle counterclockwise by \[{{45}^{\circ }}\]we will get the second arm in first quadrant and an angle of \[{{45}^{\circ }}\].
Similarly If we rotate the angle clockwise by \[{{45}^{\circ }}\] we get an angle of negative \[{{45}^{\circ }}\] .
Now note that one full rotation is ${{360}^{\circ }}$. Hence if we rotate the angle by ${{360}^{\circ }}$ or $-{{360}^{\circ }}$ we get the angle as before.
Now let us draw a standard angle of ${{300}^{\circ }}$.
Since the angle is in standard position we will take one arm of angle on x axis and then rotate the other arm by ${{300}^{\circ }}$ counterclockwise.

Now let us understand what coterminal angles are.
Coterminal angles are also standard position angles with same terminal arms.
Hence to find coterminal angles we can add and subtract ${{360}^{\circ }}$ to the given angle.
Given angle is ${{300}^{\circ }}$
Hence Coterminal angles are ${{300}^{\circ }}-{{360}^{\circ }}=-{{60}^{\circ }}$ and ${{300}^{\circ }}+{{360}^{\circ }}={{660}^{\circ }}$
Hence ${{660}^{\circ }}$ and $-{{60}^{\circ }}$ are the coterminal angles of the given angle.

Note: Now note that we can find a series of coterminal angles by adding or subtracting ${{360}^{\circ }}$ again and again. Hence we get different coterminal angles of x by ${{x}^{\circ }}\pm 360n$ where n is any natural number and hence there are an infinite number of coterminal angles for a given angle.