Video Transcript
Find one angle with positive
measure and one angle with negative measure which are coterminal to an angle
with measure two π over three radians.
Letβs consider the angle two π
over three radians. We could convert this into
degrees by using the fact that π radians is equal to 180 degrees. Two-thirds of 180 degrees
equals 120 degrees, so two π over three radians equals 120 degrees. However, we will keep our angle
in radians in this question. As our angle is positive, we
need to measure the angle in a counterclockwise direction from the initial side
as shown.
We recall that coterminal
angles share the same initial and terminal sides. This means that we need to find
alternative ways to express the same angle. We can calculate coterminal
angles by adding or subtracting two π radians from the given angle. To find another positive angle,
we need to keep measuring in the counterclockwise direction. This means that we need to add
two π radians to our angle. Two π radians is equivalent to
six π over three radians. This means we need to add two
π over three and six π over three. This is equal to eight π over
three radians. An angle with positive measure
which is coterminal to an angle with measure two π over three is eight π over
three radians.
In a similar way, we can find
an angle with negative measure by moving in a clockwise direction. This means that we need to
subtract two π from our angle. Two π over three minus six π
over three is equal to negative four π over three. An angle with negative measure
which is coterminal to an angle with measure two π over three is negative four
π over three radians. The two angles are eight π
over three and negative four π over three.
