1. ## Sine and Cosine

My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

Question:

sin(11pi/2)
= sin (3pi/2 + 8pi/2)
= sin (3pi/2 + 4pi)
= sin (3pi/2) <--- i don't know why 4pi just disappears.
= -1

Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.

2. ## Re: Sine and Cosine

Originally Posted by qwerty999
My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

Question:

sin(11pi/2)
= sin (3pi/2 + 8pi/2)
= sin (3pi/2 + 4pi)
= sin (3pi/2) <--- i don't know why 4pi just disappears.
= -1

Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.
Using a diagram of the Unit Circle, centre (0,0) and radius equal to 1 unit,
the vertical co-ordinate of a point on the circumference is the Sine of the angle.

When the angle is zero, the vertical co-ordinate is zero.
When the angle is 90 degrees, the vertical co-ordinate is 1.
When the angle is 180 degrees, the vertical co-ordinate is 0.
When the angle is 270 degrees, the vertical co-ordinate is -1.

Another 90 degrees on and we are back where we started.
Hence any multiple of 360 degrees added to the angle gives us the same vertical co-ordinate.
Knowing the periodicity allows you to determine the Sine of your given angle
by subtracting 360 degrees twice.

3. ## Re: Sine and Cosine

Originally Posted by qwerty999
My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

Question:

sin(11pi/2)
= sin (3pi/2 + 8pi/2)
= sin (3pi/2 + 4pi)
= sin (3pi/2) <--- i don't know why 4pi just disappears.
= -1

Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.
It's because the angle $\displaystyle \frac{3\pi}{2} + 4\pi$ is in the same position as the angle $\displaystyle \frac{3\pi}{2}$, you've just moved around the unit circle twice before getting to it. That means their sines are equal.