# Find the requested function value meeting all of the given conditions??

• Aug 27th 2012, 10:37 AM
Find the requested function value meeting all of the given conditions??
I have to do this packet for an AP class I'm taking, and my teacher didn't give me anything to work with. I'm desperate.

sin(theta)= (square root)3/2 and tan(theta) > 0 ; Find cos(theta).
• Aug 27th 2012, 11:06 AM
MaxJasper
Re: Find the requested function value meeting all of the given conditions??
Darw a circle with radius=1 and center at (0,0) then on sin axis go up as much as squrt(3)/2, draw a horizontal line to intersect circle at two points...now draw tan axis and check which of the two points on circle qualifies for tan>0
• Aug 27th 2012, 12:34 PM
Soroban
Re: Find the requested function value meeting all of the given conditions??

Quote:

$\sin\theta\,=\,\frac{\sqrt{3}}{2}\,\text{ and }\,\tan\theta > 0.\;\;\text{ Find }\,\cos\theta.$

$\sin\theta$ is positive: . $\theta$ is in Quadrant 1 or Quadrant 2.

$\tan\theta$ is positive: . $\theta$ is in Quardrant 1 or Quadrant 3.

. . Hence, $\theta$ is in Quadrant 1.

$\sin\theta \:=\:\frac{\sqrt{3}}{2} \:=\:\frac{opp}{hyp}$

$\theta$ is in a right triangle with: . $opp = \sqrt{3},\;hyp = 2$
Pythagorus tell us that: . $adj = 1$

Therefore: . $\cos\theta \:=\:\frac{adj}{hyp} \:=\:\frac{1}{2}$

• Aug 27th 2012, 01:11 PM
Re: Find the requested function value meeting all of the given conditions??

cos(theta) = - [(square root)2]/2 and tan(theta) < 0 ; find cot(theta) ?
• Aug 27th 2012, 05:27 PM
skeeter
Re: Find the requested function value meeting all of the given conditions??
Quote:

cos(theta) = - [(square root)2]/2 and tan(theta) < 0 ; find cot(theta) ?

did you not learn this in your pre-AP class?

you are expected to already know the values for sine and cosine on the unit circle and the definitions/identities for basic all six trig ratios ...

http://media.wiley.com/Lux/83/323183.image0.jpg
• Aug 27th 2012, 07:28 PM
Re: Find the requested function value meeting all of the given conditions??
It was actually recommended that I skip Pre-Calculus and go straight to AP Calculus AB. I was given a summer packet with these problems specifically so I could learn how to do these things.
• Aug 27th 2012, 09:09 PM
Prove It
Re: Find the requested function value meeting all of the given conditions??
Why was this recommended? The only way I would recommend something like this is if you have shown that you already know how to do the topics in Pre-Calculus...
• Aug 28th 2012, 02:56 AM
skeeter
Re: Find the requested function value meeting all of the given conditions??
Quote: