Prelim 2016 Maths Help Thread (1 Viewer)

[eyeseeyou]

Does anyone ere know why a cos wave starts from 1 and why a sine wave starts from 0

Thanks

 

[InteGrand]

Does anyone ere know why a cos wave starts from 1 and why a sine wave starts from 0

Thanks

By definition of cos and sin.

 

[nerdasdasd]

Does anyone ere know why a cos wave starts from 1 and why a sine wave starts from 0

Thanks

Read your textbook

 

[eyeseeyou]

It says the max and min value of sinx and cosx and 1 and -1 respectively so we say their amplitude in 1

@Integrand, by definition of a cos wave, it starts at one

By definition of a sine wave, it starts at 0

Please correct me if I am wrong (I can't find it in the textbook)

Thanks

 

[leehuan]

It says the max and min value of sinx and cosx and 1 and -1 respectively so we say their amplitude in 1

@Integrand, by definition of a cos wave, it starts at one

By definition of a sine wave, it starts at 0

Please correct me if I am wrong (I can't find it in the textbook)

Thanks

Yes lol...

Literally punch sin(0) and cos(0) into your calculator.



If you want the formal geometric interpretation that's a tiny bit harder.

 

[Paradoxica]

Does anyone ere know why a cos wave starts from 1 and why a sine wave starts from 0

Thanks

By convention.

We are not rewriting 60 million textbooks just because you want to change the starting values of the trigonometric functions.

Think before you post.

 

[eyeseeyou]

Yes lol...

Literally punch sin(0) and cos(0) into your calculator.



If you want the formal geometric interpretation that's a tiny bit harder.

Thanks

 

[InteGrand]

It says the max and min value of sinx and cosx and 1 and -1 respectively so we say their amplitude in 1

@Integrand, by definition of a cos wave, it starts at one

By definition of a sine wave, it starts at 0

Please correct me if I am wrong (I can't find it in the textbook)

Thanks

The textbooks sometimes don't really go through the definition of cos and sin (I do think they are in the Year 11 3U Pender (Cambridge) Textbook though, so check that out if you have it). For HSC purposes, for a real number t, cos(t) and sin(t) are defined as follows:

Draw the unit circle in the Cartesian Plane (radius 1, centred at origin). Draw a ray from the origin making an angle t radians (counter-clockwise) from the positive x-axis. This ray cuts the circle at one (and only one) point P. Then the x-value of this point is defined as cos(t), and the y-value as sin(t).

In other words, cos(t) is the x-value of the point of intersection with the ray of angle t and the unit circle, and sin(t) is the y-value.

See for example this image: http://superintendentemily.weebly.com/uploads/2/3/5/1/23512632/5027961_orig.gif .

So using these definitions, you should be able to easily show that cos(0) = 1 and sin(0) = 0.

(If we use a circle of radius r instead of unit circle, we get instead cos(t) = x/r, and sin(t) = y/r, where (x,y) is the point of intersection with the aforementioned ray and the circle of radius r centred at the origin.)

(If t is negative, go -t clockwise for the ray.)

 

[eyeseeyou]

The textbooks sometimes don't really go through the definition of cos and sin. For HSC purposes, for a real number t, cos(t) is defined as follows:

Draw the unit circle in the Cartesian Plane (radius 1, centred at origin). Draw a ray from the origin making an angle t radians (counter-clockwise) from the positive x-axis. This ray cuts the circle at one (and only one) point P. Then the x-value of this point is defined as cos(t), and the y-value as sin(t).

In other words, cos(t) is the x-value of the point of intersection with the ray of angle t and the unit circle, and sin(t) is the y-value.

See for example this image: http://superintendentemily.weebly.com/uploads/2/3/5/1/23512632/5027961_orig.gif .

So using these definitions, you should be able to easily show that cos(0) = 1 and sin(0) = 0.

(If we use a circle of radius r instead of unit circle, we get instead cos(t) = x/r, and sin(t) = y/r, where (x,y) is the point of intersection with the aforementioned ray and the circle of radius r centred at the origin.)

Thanks

 

[Green Yoda]

Does anyone ere know why a cos wave starts from 1 and why a sine wave starts from 0

Thanks

WHY IS THE ORIGIN AT (0,0) and not (-2,7)?????
WHY IS THE Y INTERCEPT WHEN X=0 AND NOT WHEN X=-23??
WHY IS WHY CALLED WHY????
WHY ARE YOU ASKING SUCH MUNTED QUESTIONS LMAO???

 

[strawberrye]

WHY IS THE ORIGIN AT (0,0) and not (-2,7)?????
WHY IS THE Y INTERCEPT WHEN X=0 AND NOT WHEN X=-23??
WHY IS WHY CALLED WHY????
WHY ARE YOU ASKING SUCH MUNTED QUESTIONS LMAO???

You are falling into eyeseeyou's trap-it is probably exactly what he wants-to aggravate people by asking such questions. Just ignore him.

 

[Sien]

WHY IS THE ORIGIN AT (0,0) and not (-2,7)?????
WHY IS THE Y INTERCEPT WHEN X=0 AND NOT WHEN X=-23??
WHY IS WHY CALLED WHY????
WHY ARE YOU ASKING SUCH MUNTED QUESTIONS LMAO???

The existential crisis is real

Sent from my D6503 using Tapatalk

 

[Nailgun]

Imagine if one day eyeseeyou comes out and is like, it was all an act to troll, I'm actually just a normal dude who enjoys fucking with people lel

tbh I would rep for days

 

[Green Yoda]

I am not even mad..I just crack up everytime

 

[Green Yoda]

Express x(x-1) in the form p+q(x-1)+r(x-1)^2
I am not sure what the question is asking me to do here.

 

[Paradoxica]

Express x(x-1) in the form p+q(x-1)+r(x-1)^2
I am not sure what the question is asking me to do here.

Expand everything and equate coefficients.

 

[Orwell]

At this point I can't tell whether eyeseeyou is a little slow or a master troll.

 

[InteGrand]

Express x(x-1) in the form p+q(x-1)+r(x-1)^2
I am not sure what the question is asking me to do here.

 

[HeroicPandas]

Express x(x-1) in the form p+q(x-1)+r(x-1)^2
I am not sure what the question is asking me to do here.

Another method is to complete the square:

 

[Green Yoda]

Just confirming something
Is the answer for sqrt((3x+2)(x-3))<|x+3|, -1<x<15/2?