All Answers

#1

+118725

+10

think about the first quadrant of a unit circle..

The unit circle is the circle with a radius of 1 and a centre of (0,0)

The fist quadrant covers angles 0 to pi/2.

At first only consider proper acute angles.

You should watch this video - it is very good. :)

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

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

$$\\cos \theta = \frac{adj}{hyp}\\\\
$but the hypotenuse is the radius of the circle so it is 1$\\\\
so\\
cos \theta = \frac{x}{1}=x\\\\
$By the same type of logic you can see that$\\\\
sin\theta = y$$

now just follow this for all angles.

With regards to the unit circle.

$$cos\theta$$ is given by the x value

and

$$sin\theta$$ is given by the y value.

If you develope a good understanding of the unit circle and what it represents senior trig will be easier.

MelodyMar 16, 2015

#1

+33666

+5

Here's a direct proof:

(An alternative would be a proof by induction.)

.

AlanMar 16, 2015

#2

+4

0

Math is everywhere and it is at a store and it is all ways it is anywhere

blystone18Mar 16, 2015

#2

+72

0

Ok so is that only one thing they have In common is they are all one triangle

Blystone4Mar 16, 2015

#1

+118725

+5

MATHS IS EVERYWHERE!!!

https://www.youtube.com/watch?v=Q2bF26372gk

MelodyMar 16, 2015

#2

+33666

+5

I guess this is looking for the height, H.

For a rectangular pyramid: V = L*W*H/3, so:

88 = 8*4.6*H/3

11*3/4.6 = H

H ≈ 7.2m

.

AlanMar 16, 2015

#1

+118725

+5

what is the question?

MelodyMar 16, 2015

#1

+118725

+5

Start by multiplying both sides by 6*7 (42) this will get rid of all the fractions.

Remember to put the LHS in brackets first. :)

MelodyMar 16, 2015

#1

+118725

+5

I am not sue that I am understanding this properly but

Proposition Y states that the money is behind door A or B

if Y is not tue then the money cannot lie behind A or B which means that proposition X must also be untrue.

(it would also mean that there was no money)

BUT

we are told that either X or Y is true so therefore Y must be true and there must be money behind A or B.

If Y is true then X must be false so the money is not behind door A.

THEREFORE

The money must be behind door B. Since I want the money I shall open door B

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

I probably did not understand the question properly because I did not even need to make it this complicated.

X : it is behind A

Y: it is behind A or B

only one is true so it must be behind B

MelodyMar 16, 2015

#1

+118725

+5

http://en.wikipedia.org/wiki/Hyperbolic_function

MelodyMar 16, 2015

#1

+118725

+5

$$\\(2x+1)(4x-3)\\
=2x(4x-3)+1(4x-3)\\
=8x^2-6x+4x-3\\
=8x^2-2x-3$$

.

MelodyMar 16, 2015

#1

+118725

+5

That is a shocker of a description. ;)

MelodyMar 16, 2015

#463

+118725

+8

@@ End of Day Wrap Mon 16/3/15 Sydney, Australia Time 10:25 pm ♪ ♫

Good evening, (๑‵●‿●‵๑)

Our magnificent answerers today were Gibsonj338, Shaomada, CPhill, Alan, Heureka, Bertie and Rosala.

A great big thank you to each of you.

Interest Posts:

1) What is the difference between a cat and a comma? Thanks anon.

2) Solving a difficult inequality Thanks Melody and CPhill

3) Tricky trig derivative. Thanks Melody and CPhill

4) Geometry Not answered.

♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫

MelodyMar 16, 2015

#2

+5

Yep, this is all the information I got. :l

GuestMar 16, 2015

#1

+118725

+5

Why is RS negative? Isn't it a length?

Are you sure you have included ALL the information. It looks like something is missing to me.

MelodyMar 16, 2015

#270

+118725

0

Tues 17/3/15

1) The Monty Hall problem. Yes again LOL I found a cool clip for it.

2) Finding volume of an odd shape. Melody

3) What is the last digit of pi? Thanks TayJay, anon and Heureka

4) Manipulating algebra Thanks CPhill and anon

5) Physics - Force and Power. Thanks Alan

6) Probability (secret santa) Melody

7) Fining an angle using sine rule Thanks melody and CPhill.

♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫

MelodyMar 16, 2015

#2

+118725

+5

Thanks CPhill, I just want to see if I can do it too. (๑‵●‿●‵๑)

Mmm that looks tricky.

let

$$y= -6*sec(sin(5x^2+3x+2))$$

let

$$\\g = sin(5x^2+3x+2)\\\\
\frac{dg}{dx}=(10x+3)[cos(5x^2+3x+2)]\\\\\\
y=-6sec(g)\\\\
y=-6(cos(g))^{-1}\\\\
\frac{dy}{dg}=6(cos(g))^{-2}(-sin(g))\\\\
\frac{dy}{dg}=\frac{-6sin(g)}{cos^2(g)}\\\\\\
\frac{dy}{dx}=\frac{dy}{dg}\times \frac{dg}{dx}\\\\
\frac{dy}{dx}=\frac{-6sin(g)}{cos^2(g)}\times (10x+3)[cos(5x^2+3x+2)]\\\\$$

$$\\\frac{dy}{dx}=\frac{-6sin(g)(10x+3)[cos(5x^2+3x+2)]}{cos^2(g)}\\\\ \frac{dy}{dx}=\frac{-6sin(sin(5x^2+3x+2))(10x+3)[cos(5x^2+3x+2)]}{cos^2(sin(5x^2+3x+2))}\\\\ \frac{dy}{dx}=-6tan(sin(5x^2+3x+2)sec(sin(5x^2+3x+2))(10x+3)[cos(5x^2+3x+2)]}\\\\
\frac{dy}{dx}=-(60x+18)tan(sin(5x^2+3x+2)sec(sin(5x^2+3x+2))[cos(5x^2+3x+2)]}\\\\$$

WOW this is the same as CPhill's answer (๑‵●‿●‵๑)

MelodyMar 16, 2015

#13

+118725

0

Nope. I think we need YOUR answer now Rosala. :)

MelodyMar 16, 2015

#4

+118725

+5

Thanks Heureka,

That site seems to refer to the unit of weigth as pounds force. :)

so I assume that pounds is a measure of mass and pounds force is a measure of weight. ?

MelodyMar 16, 2015

#3

+118725

+5

So it does - thanks Alan.

The quadratic formula will still work though. :)

MelodyMar 16, 2015

#1

+118725

+5

I have no idea, could you please check that all the terms are correct?

MelodyMar 16, 2015

#1

+118725

+5

1) start by multiplying both sides by (40-x)

2) then simplify both sides seperately

3) then think about it.

MelodyMar 16, 2015

#1

+118725

0

Good one anon :)

MelodyMar 16, 2015

#1

+11912

+5

ok so lets do it like this

x+4=7

now take 4 to the other side and subtract from, 7 to get x

x= 7-4

x= 3

now to checkt he answer put 3 in place of x and see if we get 7

3+4

= 7

yay....we got the value of x

rosalaMar 16, 2015

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MATHS IS EVERYWHERE!!!

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