Taylor's 4th Blog

These are the notes on what we learned in section 7.5

You will need to know the following so that you can work out the equations.

Tan Theta=y/x
Cot Theta = x/y
Sec Theta = r/x
Csc Theta = r/y

Ok now that we know what Tan, Cot, Sec, and Csc are lets use them to solve the following equations.

Since Sin Theta = 4/6 0<> 90 degrees find the meaning of the other five trig functions.

(REMEMBER I DON’T KNOW HOW TO PUT A GRAPH ON THE COMPUTER SO I WILL JUST TYPE IT OUT.)

Ok, we know the since Sin is positive then the y needs to be positive and that can only happen on the second and first quadrant. Also since 4/6 is supposed to be less than 90 degrees we need to be in the first quadrant. Ok now we need to find x. You can draw a triangle and put in the info that you know to help you.

A^2+4^2=6^2

We will use the Pythagorean theorem to help us find x.

A^2+16=36
a^2=20

We will then use the exponents to get theses answers and then we will subtract 16 from 36 and get 20 then we will square the a and 20 and the answer will be the square root of 20.

Now we just fill in the blanks.

Cos x/r= square root of 20/6

Tan y/x= (since we can’t have a square root at the bottom we will multiply it by the square root of 20 and reduce and get this) square root of 20/5

Cot x/y= square root of 20/4

Sec r/x=(since we can’t have a square root at the bottom we will multiply it by the square root of 20 and reduce and get this) 3 times the square root of 20/10

Csc r/y = 6/4 (reduced is) 3/2

Now lets try to find the reference angle of tan.

Find the reference angle for Tan 65 degrees.

First we find what quadrant its in. Which is the first because of the degrees which means tan is positive.

Tan 65 degrees

Since 65 degrees is already in-between 0 and 90 degrees we don’t need to subtract and since it’s not on the Trig chart that means that Tan 65 degrees is your answer.

That is what I learned in 7.5. Until next time!