HELP PLEASE!!!

[elizabeth292]

i am so confused in my math class right now. i have no idea what to do or how to start. it just doesnt make sense. i am going to go in for tutoring but the assignment is due tommorrow morning and i need to get a good score otherwise my grade will go way down. so if anyone can help me i will be SO grateful.

i need to find the smallest positive number for which:

1. sin (2x)-sin x=0
2. sin (x+1)= sin x
3. sin x+ cos (2x)=0
4. sin x-cos (2x)=0

(in radians..)

-elizabeth

 

[Daniel_Feldman]

I'll show you the first one-see if you can work with the rest.



sin (2x)-sin x=0


Double angle formula:

sin(2x)=2sin(x)cos(x)

2sin(x)cos(x)-sinx=0

sin(x)(2cos(x)-1)=0


sin(x)=0

Smallest positive value for which this is true:

x=pi

Note: x=0 does not work because we need the smallest positive number, not the smallest nonnegative number. So x must be greater than 0.

2cos(x)-1=0

cos(x)=1/2

Smallest positive value of x for which this is true: x=pi/3



Now, of these two values (pi and pi/3), which is smaller? That's your answer.

 

[galactus]

i am so confused in my math class right now. i have no idea what to do or how to start. it just doesnt make sense. i am going to go in for tutoring but the assignment is due tommorrow morning and i need to get a good score otherwise my grade will go way down. so if anyone can help me i will be SO grateful.

i need to find the smallest positive number for which:

1. sin (2x)-sin x=0

One way is Newton's method.

Let 1 be your initial estimate.

$\displaystyle 1-\frac{sin(2(1))-sin(1)}{2cos(2(1))-cos(1)}=1.04941471712$

$\displaystyle 1.04941471712=\frac{sin(2(1.04941471712))-sin(1.04941471712)}{2cos(2(1.04941471712))-cos(1.04941471712)}=1.40720178129$

$\displaystyle 1.40720178129-\frac{sin(2(1.40720178129))-sin(1.40720178129)}{2cos(2(1.40720178129))-cos(1.40720178129)}=1.0471975512={\pi}/3$


2. sin (x+1)= sin x

Use the addition formula:

$\displaystyle sin(x+1)=sin(x)cos(1)+cos(x)sin(1)$

$\displaystyle sin(x)cos(1)+cos(x)sin(1)=sin(x)$

$\displaystyle sin(x)cos(1)+cos(x)sin(1)-sin(x)=0$

Factor:

$\displaystyle sin(x)(cos(1)-1)+cos(x)sin(1)=0$

$\displaystyle (cos(1)-1)sin(x)=-sin(1)cos(x)$

$\displaystyle \frac{(cos(1)-1)}{-sin(1)}=\frac{cos(x)}{sin(x)}$

$\displaystyle tan(1/2)=cot(x)$

$\displaystyle x=cot^{-1}(tan(1/2))=\frac{({\pi}-1)}{2}$

There, Dan and I gave you two answers. Can you struggle through the other two?.
3. sin x+ cos (2x)=0
4. sin x-cos (2x)=0

(in radians..)

-elizabeth

 

[elizabeth292]

wow that helped out so much. i think that i was just stuck and had no idea where to go or what to do... i was able to get the other two problems. thanks a lot everyone!!