7-5 The other trig functions

Section 7-5 is the same as section 7-4, but with tan, cot, sec, and csc, instead of using sin and cos. It is not that hard since you are pretty much doing the same thing as 7-4.

First off you need to know what does tan, cot, sec, and csc equal too. Tan equals to y/x. Cot equals to x/y. *Notice how Tan and Cot are opposite from each other. Sec equals to r/x which is the opposite of cos. Csc equals to r/y and is the opposite of sin.

Since this section is pretty much the same as section 7-4, I won't give the steps. I will just explain as I go. I will do an example for each function and do two negative degrees and two positive degrees.

Ex. 1. Tan 210 degrees

1. 210 is in quadrant three.
2. Tan = y/x = +ve/-ve = -ve. It is negative because in the third quadrant the y coordinate is positive and the x coordinate is negative. If you divide a positive by a negative, it will give you a negative.
3. Now to find the reference angle, you will subtract 180 from 210. So 210 - 180 = 30.
   
4. So the reference angle for Tan 210 degrees is -Tan 30 degrees.

Ex. 2 Sec 125 degrees.

1. 125 is in quadrant two because it is between 90 and 180 degrees.
2. Sec = r/x = 1/+ve = +ve. It is positive because the x coordinate is positive and when you divide 1 by a positive you get a positive number.
3. Now you have to find the reference angle. 125-180 = -55. Since it is negative, you have to take the absolute value of it. The absolute value of -55 is 55.
4. The reference angle for Sec 125 degrees is +Sec 55 degrees.

Ex. 3 Cot -220 degrees.

1. -220 is in quadrant two. Since it is negative you go backwards. So 90 degrees would be quadrant four, 180 degrees would be quadrant three, 270 degrees would be quadrant two, and 360 degrees would be in quadrant one.
2. Cot = x/y = +ve/-ve = -ve.
3. You do not want to use the -220 to subtract from 180 because that would just give you a bigger number. So you use 220 and subtract from 180 which will give you 40.
4. The reference angle for Cot -220 degrees is -Cot 40 degrees.

Ex. 4 Csc -150 degrees

1. -150 is in quadrant three. Like I said in the example before this one, you go backwards since it is negative.
2. Csc = r/y = 1/-ve = -ve.
3. Again, like I said in the example from above don't use the -150 to subtract. So 150-180 = -30. Since it is a negative answer, you take the absolute value of it which gives you 30.
4. The reference angle for Csc -150 degrees = -Csc 30 degrees.

That is how you find a reference angle for the other trig functions, it is not that hard since in the last section, we learned how to find a reference angle for sin and cos. It is the same thing, just with different trig functions.

-Amber :)