## October 23, 2006

### Scribe Post, Trig Identities

Hey you guys, it's JessicaJill, and I was your scribe for today's double class. In the morning we had a five question quiz to do in 5 minutes. Here it is.

1. secΘ - tanΘ is identical to:

a) cosΘ/1 + sinΘ
b) sinΘ/1 + cosΘ
c) secΘtanΘ
d) cotΘcscΘ
e) None of these

SOLUTION: The answer is a. Here's why:

2. 1 - cos2Θ/1 + sinΘ is identical to:

a) cosΘ
b) tanΘ
c) sinΘ
d) cosΘ/1 + sinΘ
e) sinΘ/1 - cosΘ

3. 1- sec2Θ is identical to:

a)-tan2Θ
b)tan2Θ
c)cot2Θ
d)-csc2Θ
e)cos2Θ
We know that tan²θ + 1 = sec²θ, given by the pythagorean identity. By switching things around we can get that tan²θ = sec²θ - 1, and that -tan²θ = -sec²θ + 1, which can also be read as -tan²θ = 1 - sec²θ.

4. Given than cosΘ = -1/3 and sinΘ is greater than 0, then sinΘ equals

a) -(2√2)/3

b) (2√2)/3
c) -√10/3
d) √10/3
e) 1/3

5. Given that cscΘ = -4, Θ is greater than π and less than 3π/2, then tanΘ equals

a) √3/4
b) -√15/15
c) -4
d) 4
e) √15/15

Because a majority of the class had a little difficulty with these questions, it wasn't worth marks.

Then we were given three questions on the board to solve:

In our afternoon class we got some notes to put into our math dictionaries.

We then were given 5 questions on the board, all that were on (a) previous exam(s), but didn't have enough time to go through the answers in class, so we were told to do it for homework.

QUESTIONS

1. Solve for θER in radians to 3 decimal places [calculator allowed]:

4cos(2θ) + 3 = 0

2. Simplify tanθ/cscθ

3. α and β are quadrant II angles, sinα = 1/3 and sinβ = 2/3. Find the exact value of cos(α + β).

4.Write and equivalent expression: cos(3x)cos(2x) + sin(3x)sin(2x)

5. Prove: (1/1 - sinθ) + (1/1 + sinθ) = 2tan²θ + 2

Well, that's it. Sorry it took me so long to get it up. I had a lot of work in the last week and I wanted everything to be perfect. This post is still a little incomplete, but I wanted it to be published already.