(adsbygoogle = window.adsbygoogle || []).push({}); different (easy) math questions before my exam :)

1.

1. The problem statement, all variables and given/known data:

Write as simple as possible: 2 sinv cosv-sinv

------------------

cos^2v-sin^2v-cosv+1

(cos^2v same as (cosv)^2)

2. Relevant equations:

sinv

tanx= -----

cosv

cos^2v+sin^2v = 1

3.

Sollution my previous helper says:

cos^2v-sin^2v is supposed to be 2cos^2v - 1.

Because: cos2x=cos^v-sin^2v (?)

=2cos^2-1 ((and solves it easy after that))

How's that?

My attempt at a solution:

2 sinv cosv-sinv

------------------

cos^2v-sin^2v-cosv+1

sinv(2cosv-1)

----------------

cos^2v-(1-cos^2v) -cosv+1

sinv(2cosv-1)

----------------

2cos^2v-cos v

... and then I don't know what to do. I can't just delete one cosv in each part because it's one 2cos^2v there, and it's different..

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2.

1. The problem statement, all variables and given/known data:

This is inside a test ((64+t^2)^2)` it's supposed to be: 2(64+t^2) x 2t.

2. Relevant equations:

My helped reffered to that (u^n)` = n*u` * u^n-1. Which gives the above result. I don't see that law in my 2mx book, is it 3mx? But this is a 2mx test. My book though states that (x^n)`= n*u^n-1 (eg: (-6x^2)`= -12x) , but that doesn't go for biggies like (64+t^2), am I right?

3. The attempt at a solution:

My main question is just where is that law from?

3.

1. The problem statement, all variables and given/known data:

When do you use {and ( together, like: {(u)} ?

4.

1. The problem statement, all variables and given/known data & Relevant equations & The attempt at a solution:

My book states that 3[squareroot](-5)^3 = -5, and that 4[squareroot](-5)^4 = 5, and so on in odd and even numbers. But laters say that 4[squareroot]a^4, when a is a negative number(as in -5 above) gets to be -a. As if 4[squareroot](-5)^4 = 5, but even numbers should give positive results. Why does it change?

5.

1. The problem statement, all variables and given/known data

How do you solve tanx<1 nicely on paper?

The problem statement is tanx<1

2. Relevant equations:

sinv

tanx= -----

cosv

tan(v+k 180') = tanv

3. The attempt at a solution

tanx<1

x<45'(degrees) and x<225'(degrees)

L=<45',0'> and <90',225'> and <270,360'>

But my counting seems so short. Is there any rules that say that I'm writing too short, then if so what am I missing?

All help appreciated! :) Hope I placed this at the right place

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# Homework Help: Different (easy) math questions before my exam

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