Angles - Trigonometry

First lets identify the different quadrants.

Quadrant I:

Quadrant II:

Quadrant III:

Quadrant IV:

Now looking at our possible answer choices, we will add or subtract until we get the reduced fraction of the angle. This will tell us which quadrant the angle lies in.

thus in quadrant III.

thus in quadrant III.

Therefore,

and is the correct answer.

These angles are supplementary, as the sum of the angles is 180o.

Each quadrant represents a change in radians. Therefore, an angle of radians would pass through quadrants , , and end in quadrant . The movement of the angle is in the clockwise direction because it is negative.

Each quadrant represents a change in degrees. Therefore, an angle of radians would pass through quadrants , , , and end in quadrant . The movement of the angle is in the clockwise direction because it is negative.

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a second quadrant angle. Since is between and , it is a second quadrant angle.

First we can write:

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between and , the angle is a second quadrant angle. Since is between and , it is a second quadrant angle.

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between and , the angle is a third quadrant angle. Since is between and , it is a thrid quadrant angle.

First we can convert it to degrees:

The movement of the angle is clockwise because it is negative. So we should start passing through quadrant . Since is between and , it ends in the quadrant .

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a first quadrant angle. Since is between and , it is a first quadrant angle.

First we can convert it to degrees:

When the angle is more than we can divide the angle by and cut off the whole number part. If we divide by , the integer part would be and the remaining is . Now we should find the quadrant for this angle.

When the angle is between and , the angle is a third quadrant angle. Since is between and , it is a third quadrant angle.

The second quadrant contains angles between and , plus those with additional multiples of . The angle is, after subtracting , is simply , which puts it in the second quadrant.

When we think of angles, we go clockwise from the positive x axis.

Thus, for negative angles, we go counterclockwise. Since each quadrant is defined by 90˚, we end up in the 3rd quadrant.

The angle 315 degrees is located in the fourth quadrant. The correct coordinate designating this angle is .

The tangent of an angle is .

Therefore,

First lets identify the angles that make up the third quadrant. Quadrant three is to or in radians, to thus, any angle that does not fall within this range is not in quadrant three.

Therefore, the correct answer,

is not in quadrant three because it is in the first quadrant.

This is clear when we subtract

.

First lets identify the different quadrants.

Quadrant I:

Quadrant II:

Quadrant III:

Quadrant IV:

The correct answer,, is coterminal with .

We can figure this out by adding , or equivalently to get , or we can count thirds of pi around the unit circle clockwise. Either way, it is the only angle that ends in the second quadrant.

is coterminal with the angle , or . This splits quadrants I and II:

One way to uncover which quadrant this angle lies is to ask how many complete revolutions this angle makes by dividing it by 360 (and rounding down to the nearest whole number).

With a calculator we find that makes full revolutions. Now the key lies in what the remainder the angle makes with revolutions:

, therefore our angle lies in the fourth quadrant.

Alternatively, we could find evaluate and .

The former (sine) gives us a negative number whereas the latter (cosine) gives a positive. The only quadrant in which sine is negative and cosine is positive is the fourth quadrant.

Step 1: Define the quadrants and the angles that go in:

QI:

QII:

QIII:

QIV:

Step 2: Find the quadrant where is:

The angle is located in QII (Quadrant II)

First, using the unit circle, we can see that the denominator has a four in it, which means it is a multiple of .

We want to reduce the angle down until we can visualize which quadrant it is in. You can subtract away from the angle each time (because that is just one revolution, and we end up at the same spot).

If you subtract away twice, you are left with , which is in quadrant I.

.

According to the unit circle, an angle of is similar to an angle of .

Therefore: