- #1
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different (easy) math questions before my exam :)
1.
1. Homework Statement :
Write as simple as possible: 2 sinv cosv-sinv
------------------
cos^2v-sin^2v-cosv+1
(cos^2v same as (cosv)^2)
2. Homework 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..
[/b]
2.
1. Homework Statement :
This is inside a test ((64+t^2)^2)` it's supposed to be: 2(64+t^2) x 2t.
2. Homework 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. Homework Statement :
When do you use {and ( together, like: {(u)} ?
4.
1. Homework Statement & 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. Homework Statement
How do you solve tanx<1 nicely on paper?
The problem statement is tanx<1
2. Homework 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
1.
1. Homework Statement :
Write as simple as possible: 2 sinv cosv-sinv
------------------
cos^2v-sin^2v-cosv+1
(cos^2v same as (cosv)^2)
2. Homework 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..
[/b]
2.
1. Homework Statement :
This is inside a test ((64+t^2)^2)` it's supposed to be: 2(64+t^2) x 2t.
2. Homework 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. Homework Statement :
When do you use {and ( together, like: {(u)} ?
4.
1. Homework Statement & 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. Homework Statement
How do you solve tanx<1 nicely on paper?
The problem statement is tanx<1
2. Homework 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