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

SOLUTION: The answer is c.

3. 1- sec²Θ is identical to:

a)-tan²Θ
b)tan²Θ
c)cot²Θ
d)-csc²Θ
e)cos²Θ

SOLUTION: The answer is a.

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

SOLUTION: The answer is a.

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

SOLUTION: The answer is e.

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:

After that, he asked us what quadrant cos2α was in from question 3, and we all had different answers. A lot of us were a little afraid of being wrong, so he put us in groups to think about what quadrant we thought it was in. With several different answers given, we came to the conclusion that it was in quadrant III. If you think about what our answer was, where's it's negative and where the related angle is, the answer is clear.

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.