math wizards of anandtech, i seek your help once again in this mind melting math problem

[RayEarth]

if sin theta=0.1, find sin(theta + pie)
theta= the greek 0
pie= 3.14...

the answer in the back of the book says -0.1, but what are the steps to solving and checking this problem?

 

[Ns1]

n/m me so stupid

and i'm supposed to be in calc2 wtf

 

[worth]

Hint: sin(theta + pie) shifts it to the left pie.

 

[Bobomatic]

umm.. in english? we usually use english in ATOT. JK I dont know

 

[worth]

<<
sin(theta + pi)
sin theta + sin pi >>



(x+2)^2 = x^2 + 2^2 in your math book, eh?

sin(a + b) = sin a cos b + cos a sin b

 

[Ns1]

sue me, i bombed trig, badly =P

 

[RaynorWolfcastle]

Take a look at the unit circle, a rotation of Pi entails a rotation of 180 degrees in the counterclockwise direction

so if you rotate an angle that's above the positive x-axis 180 degrees you will get the same angle below the negative x-axis...

hard to explain with just words, you need to look at the unit circle

-Ice

 

[RayEarth]

thanks for the replys, i'll tried to let it sink in some more, kinda confusing, i'm thinking about the unit circle, but nothing's happening, my hand is not writing anything as if my brain had no thoughts.

 

[crypticlogin]

The other way of looking at it is to plot the graph of sin(theta) from theta:0-->2pi. At some point sin(theta)=y and if you increase theta by pi, the sin value will be negative of the original, -y for any value of theta. You should be able to see this both ways, on the unit circle and in the plots.

 

[cchen]

Ok. When sin is between 0 and pi, it's positive right? So theta is between 0 and pi
sin of anything between >180 and less than 360 will be negative right?

so if you add pi to the current theta, which would be shifting theta to 180<theta<360, then it would negative

 

[S0me1X]

Just think of what angles x has to be for sin(x) to be .1
If you imagine a unit circle, the angle would have to be in the 1st or 2nd quadrant (since the ratio of sin is y/r on the unit circle)

Now, if you take sin(x+pi) then the angle would be in the 3rd or 4th quadrant, making it negative.

 

[xirtam]

Whenever you take an angle in radians and add pi to it, you're going to get the exact opposite of what you already have. It's a 180-degree turn. So multiply the x-component by negative one, multiply the y-component by negative one, and you will have flipped it 180-degrees, or added pi radians.

HTH.

 

[MichaelD]

Negative pies? Positive pies? Rotated left pie? WTH? I just like pie, period.

 

[vtqanh]

sin (pi + a) = - sin a
sin (pi - a) = sin a
cos (pi + a) = - cos a
cos (pi - a) = - cos a
sin (pi/2 + a) = cos a
sin (pi/2 - a) = cos a
cos (pi/2 - a) = sin a
cos (pi/2 + a) = - sin a
Anything else about tan and cotg you can refer to tan as sin/cos, and cotg as cos/sin
The easiest steps to solve that problems is : sin (pi + theta) = sin pi x cos theta + sin theta x cos pi
sin pi is 0, and cos pi is - 1, that's why u get - sin theta, which is -0.1