Helen's Blog

This week I learned how to convert and find degrees and angles.


Converting Degrees to Radians

To convert degrees to radians you have to multiple the degrees x PI/180.

Ex: 110 degree= 110 x PI/180=110PI/180

Then you can simplify it by dividing 110/180=11PI/18.

Converting Degrees to Radians

To convert radians to degrees you have to multiple the radian x 180/PI.

Ex: PI/20 rads= PI/20 x 180/PI=180/20= 9 degrees


Finding Coterminal Angles

* coterminal angles +/- 360 degrees or +/- 2PI if it is in radians.

To find a positive coterminal angle you keep adding 360 until you get a positive number.

Ex: -310 degrees = -310+360= 50 degrees

To find a negative coterminal that is in radians, you would subtract the radians minus 2PI.

Ex: PI/6 - 2PI= -11/6 PI



Finding Reference Angles

1. First you would have to determine if the function is a positive or negative. To determine if the function is positive or negative then you would have to see what quadrant it would be in.

2. Subtract 180 degrees from the angle until the absolute value of the angle is between 0 and 90 degrees.

3. If you end up with a trig chart angle, then you would plug it in. If you didn't then you can leave it alone.

Ex: sin 170 degrees

It is in quadrant II so it would be positive.

170-180=-10

The absolute value of -10 = 10

So, the answer is sin 10 degrees.

Trig Chart

o degrees - 0

30 degrees- PI/6

45 degrees- PI/4

60 degrees- PI/3

90 degrees-PI/2

Converting Minutes and Seconds to Degrees

To convert to degrees: x/60 +y/3600= degrees

Ex 1: 20' 15" convert to degrees

20/60+15/3600 = .3375 degrees

Ex 2: 9 degrees 6' 48" convert to degrees

9+(6/60)+(48/3600) =9.18 degrees