# Trig Functions

• Jul 2nd 2012, 05:14 PM
computerpublic
Trig Functions
Hello, I am using the trig diagram below and I am experiencing some problems. When I enter cos(100) in my calculator, i get a negative number. According to the graph, at 100 degrees going clockwise, cosine should be positive from 90 - 180 degrees. Can someone please explain what I am doing wrong.
Thanks.

http://mathscene.co.uk/t/F/Su36k02_m06.gif
• Jul 2nd 2012, 05:26 PM
skeeter
Re: Trig Functions
positive angles are measured counter-clockwise from the positive x-axis.

100 degrees measure ccw from the positive x-axis terminates in quadrant II ... the value of cosine is negative.

... also, please post trig questions in the trig forum.
• Jul 2nd 2012, 05:32 PM
emakarov
Re: Trig Functions
In trigonometry, angles measure counterclockwise rotation. 100 degrees is a bit more than the right angle, so rotating the point (1,0) around the origin by 100 degrees counterclockwise puts it in the top-left (second) quadrant, where the cosine is negative. But even if angles were measured clockwise, 100 degrees would be in the bottom-left (third) quadrant, where the cosine is also negative.
• Jul 2nd 2012, 05:34 PM
computerpublic
Re: Trig Functions
So does that mean that zero degrees start at the point of 90 degrees clockwise?
Thanks.
• Jul 2nd 2012, 05:42 PM
skeeter
Re: Trig Functions
once again ... the initial side of an angle in standard position is the positive x-axis.

Standard Position and Reference Angles
• Jul 2nd 2012, 05:58 PM
richard1234
Re: Trig Functions
In trigonometry, 0 degrees corresponds with a 90-degree bearing (e.g. "east") and 90 degrees corresponds with 0/360 degrees ("north"). It's a little weird why it is defined that way, but it has to do with the way the x- and y-axes are labelled.
• Jul 2nd 2012, 06:25 PM
computerpublic
Re: Trig Functions
I am looking for a VERY SIMPLE function that returns a completely negative or positive number (not both positive and negative), no matter the size of the input. Is it possible? Can someone please help me.
Thanks.
• Jul 2nd 2012, 07:53 PM
richard1234
Re: Trig Functions
Quote:

Originally Posted by computerpublic
I am looking for a VERY SIMPLE function that returns a completely negative or positive number (not both positive and negative), no matter the size of the input. Is it possible? Can someone please help me.
Thanks.

I don't get what you're saying.

The unit circle is very simple to understand: angle measure increases as you move counterclockwise. The point $\displaystyle (1,0)$ corresponds with $\displaystyle \theta = 0^{\circ}$, $\displaystyle (0,1)$ corresponds with $\displaystyle \theta = 90^{\circ}$, and $\displaystyle (\sqrt{2}, \sqrt{2})$ corresponds with $\displaystyle \theta = 45^{\circ}$.

For any point $\displaystyle (x,y)$ on the unit circle, $\displaystyle \sin \theta = y$ and $\displaystyle \cos \theta = x$ (because sine and cosine are defined as opp/hyp, adj/hyp, where hyp = radius = 1). For example, $\displaystyle \sin 0^{\circ} = 0$, $\displaystyle \cos 0^{\circ} = 1$ because (1,0) corresponds with $\displaystyle 0^{\circ}$.

Therefore $\displaystyle \sin \theta \ge 0$ whenever $\displaystyle y \ge 0$ and $\displaystyle \cos \theta \ge 0$ whenever $\displaystyle x \ge 0$.
• Jul 3rd 2012, 03:00 AM
skeeter
Re: Trig Functions
Quote:

Originally Posted by computerpublic
I am looking for a VERY SIMPLE function that returns a completely negative or positive number (not both positive and negative), no matter the size of the input. Is it possible? Can someone please help me.
Thanks.

$\displaystyle y = \sin{x} + 2$ or $\displaystyle y = \cos{x} + 2$

$\displaystyle y > 0 \, ; \, \forall x$

if you want the output strictly negative, subtract the 2 (instead of adding 2) in both functions.

simple enough?
• Jul 3rd 2012, 07:52 AM
richard1234
Re: Trig Functions
Quote:

Originally Posted by skeeter
$\displaystyle y = \sin{x} + 2$ or $\displaystyle y = \cos{x} + 2$

$\displaystyle y > 0 \, ; \, \forall x$

if you want the output strictly negative, subtract the 2 (instead of adding 2) in both functions.

simple enough?

Yeah, I couldn't understand what computerpublic meant about "completely positive or completely negative" because a number cannot be both positive and negative. He should've said "positive for all x" or "negative for all x."

Anyway, $\displaystyle y = \sin x + 2$ is probably the simplest function. You could also try $\displaystyle y = \cos^2 x + 1$.
• Jul 3rd 2012, 08:15 AM
HallsofIvy
Re: Trig Functions
Quote:

Originally Posted by computerpublic
I am looking for a VERY SIMPLE function that returns a completely negative or positive number (not both positive and negative), no matter the size of the input. Is it possible? Can someone please help me.
Thanks.

The simplest such functions are |x|+ 1 and $\displaystyle x^2+ 1$. Does this have anything at all to do with your previous questions in this thread?