pre calc help please?

Question

determine quadrant in which each angle lies
1) pi/5
2) 7pi/5
3) -pi/12
4) -11pi/9

i don't understand how to get the answer at all :( please help

Answer 1

Hi,

Keep in mind pi = 180 degrees

Now imagine X and Y axis drawn and draw the following angles with the base on the X axis and the vertex on the origin,

1] pi / 5 = 180 / 5 = 34 degrees

The other arm for this angle will be in the first quadrant hence the angle lies in the first quadrant

Similarly


2] 7 pi / 5 = 7*34 = 238 >> Third quadrant

3] -pi/12 = -15 >>> Fourth Quadrant

Here you trace a reverse angle i.e. an angle with the base on the x axis and vertex at origin BUT angle is traced in the CLOCKWISE direction


4] -11pi / 9 = -220 >> Second quadrant



Keep in mind
0 to 90 >> First quadrant
91 to 180 >> Second
181 - 270 >> Third
271 - 360 >> Fourth

Answer 2

Try to remember back to Algebra II. There, something called the radian was defined, and you had a conversion formula that 2*pi radians was 360 degrees.

Also, you learned some trig, and that in angle measurement, you started measurement along the positive x-axis, and that the first quadrant (x and y both positive) included angles from 0 to pi/2 radians. Continuing counterclockwise, the second quadrant included angles from pi/2 to pi radians.
Also, angles measured counterclockwise were positive, but angles measured clockwise from zero degrees were negative.
So, you can find out the domain of angles in each quadrant, measured both positively and negatively. Then you determine where each angle fits in.
In example 3, -pi/12 lies between 0 and -pi/2 radians, and angles in this domain are in the 4th quadrant (x positive, y negative).

Answer 3

I had to search for images so that you can have a visual where the quadrants are.
If you go to:
http://www.mathsisfun.com/definitions/quadrant-graph-.html
you can see where the quadrants are.
If you go to:
http://apcsteacher.com/reference/vb/graphing/radians_vs_degrees.jpg
you can see where the radians are.

For negative numbers add 2pi to it until it becomes positive. This is just adding a complete circle and does not change anything. (Because if you are in a circle and you go a complete circle you end back up where you started) This will convert it to a positive number for you.

So.
1.) 1/5 pi is between 0 and 1/2 pi which is in quadrant 1.
2.) 7/5 pi is between 1 and 3/2 pi which is in quadrant 3.
3.)-1/12pi+2pi=(24/12 - 1/12)pi = 23/12 pi which is between 3/2 pi and 2 pi which is in quadrant 4.
4. -11/9 pi +2pi = (18/9 - 11/9)pi =7/9 pi which is between 1/2 pi and 1 pi which is in quadrant 2.

Answer 4

I'll explain and do the first and third for you... you can then do 2 and 4 yourself

Think of a circle as split into four quarters (or quadrants). The first goes from 0 to 90 degrees (clockwise), the second to 180 degrees and so on.
We also use π (pi) to denote half the circle - or 180 degrees.

Angles between 0 to π/2 are in the first quadrant.
Angles between π/2 and π are in the second quadrant
Angles between π and 3π/2 are in the third quadrant
Angles between 3π/2 and 2π are in the fourth quadrant

However - when we get to 2π we just go back to 0 again (since we have come back full circle).

Similarly - we can go backwards - and -π = π (because going 180 degrees anticlockwise is the same as going 180 degrees clockwise).

So -π/2 = 3π/2
Often in fact you only see angles measured from -π to π rather than 0 to 2π

So -π to -π/2 covers the third quadrant
and -π/2 to 0 covers the fourth quadrant

So to calculate your answers - we just work out which quadrant they belong in...
1) π/5 is less than π/2 (36 < 90 degrees) so this angle is still in the first quadrant.

2) Do yourself in the same way

3) -π/12 : If you add 2π (i.e. take it one whole revolution round again so it is the same angle - but now no longer negative) we get 23π/12
This is more than 3π/2 and less than 2π - so it is in the 4th quadrant.
Alternatively we can say it is between -π/2 and 0 so it is in the 4th quadrant

4) Do yourself in the same way

Answer 5

1 first
2 third
3 fourth
4 second

the first quadrant is from zero to pi/2 or -3pi/2 to-2pi
the 2nd is from pi/2 to pi or -pi to -3pi/2
the 3rd is from pi to 3pi/2 or -pi/2 to -pi
the fourth is from 3pi/2 to 2pi or -zero to -pi/2

Answer 6

you could always convert them to degrees and then determine the quadrant that way.

Answer 7

1) I
2) III
3) IV
4) II