Devin's Reflection #10

This week we learned some more trig stuff. We learned some trig functions. The sin and csc both deal with the y factor and radius. The cos and sec both deal with the x factor and radius. The tan and cot both deal with the x factor along and the y factor. Radius is the square root of x(2) + y(2).

The trig functions are:

sin 0= y/r

cos 0= x/r

tan 0= y/x

csc 0= r/y

sec 0= r/x

cot 0= x/y

Unit Circle

2-(0,1)-90-pi/2 1-(1,0)-0,360-0,2pi

3-(-1,0)-180-pi 4-(0,-1)-270-3pi/2

The Trig Chart

0 sin 0=0 cos 0-1 tan 0=0

30 sin pi/6=1/2 cos pi/6= (3)/2 tan pi/6=(3)/3

45 sin pi/4=(2)/2 cos pi/4=(2)/2 tan pi/4=1

60 sin pi/3=(3)/2 cos pi/3= 1/2 tan pi/3=(3)

90 sin pi/2=1 cos pi/2=0 tan pi/2= underined

0 csc 0= undefined sec 0=1 cot 0= undefined

30 sin pi/6=2 sec pi/6=(2) cot pi/6=(3)

45 sin pi/4=(2) sec pi/4=(2) cot pi/4=1

60 sin pi/3=2(3)/3 sec pi/3=2 cot pi/3=(3)/3

90 sin pi/2=1 sec pi/2=undefined cot pi/2=0

Reference angles must be between 0 and 90, 0 and pi/2

1. Find which quadrant angle is in

2. Determine the sign in that quadrant (+ve or -ve)

3. Subtract 180 until the angle is between 0 and 90, 0 and pi/2

We also learned inverses.

To solve for an angle

1. simplify any expression

2. get the trig function by itself

3. take the trig inverse of both sides

4. use chart unit circle or calculator to find 1 angle

5. set up and find other quadrants with the same sign as the value.

Ex. sin -1((2)/2)=45 quadrants 1 and 2

To make from quadrant to quadrant:

1-3 make it -ve and add 360

1-2 make it -ve and add 180

1-4 add 360

2-4 add 180