This week I’ve decided to talk about section 7-5, the other trig functions. This is probably the easiest thing we did in all of chapter seven. The processes in this section use the unit circle, the trig chart, and your knowledge of trig functions. So, if you don’t know those things you should look them over before trying this section (:

-First, you should know how to use your calculator. You have special buttons for sin, cos, and tan, but not for csc, sec, and cot. You need to know the following:

cotƟ=1/tan( )

secƟ=1/cos ( )

cscƟ=1/sin( )

EXAMPLE :Find the other 5 trig functions given tanƟ= -24/7 ∏<Ɵ<∏/2

First, you have to determine which quadrant your graph will fall in. It is easiest to do this by drawing a graph like this:

Next, you refer to your unit circle. ∏ is at (-1,0) and ∏/2 is at (0,1). Therefore, your graph will be in the second quadrant. You would then draw in your triangle and your graph will look like this:

Sincs tan=y/x, you know that the leg of the triangle on your y axis will be 24 and the leg of your triangle on the x axis will be seven. You can then find the hypotenuse using the Pythagorean Theorem. (a^2+b^2=c^2). NOTE: You do not have to use the Pythagorean Theorem if you know your triplets. Your triplets are 3,4,5 and 5,12,13 and of course 7,24,25. After determining that your hypotenuse is 25, your graph will look like this:

Based on this information, your answer will be as follows (keep in mind that your x is negative and your hypotenuse is your radius):

I like to put this here to remind myself: x= -7, y=24, r=25

sinƟ=y/r= 24/25

cscƟ=r/y=25/24

cosƟ=x/r= -7/25

secƟ= r/x= -25/7

cotƟ=x/y= -7/24

Remember that tanƟ=y/x= -24/7 was the given function J

--Sarah