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).
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).
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
Hello, MaddyV!
$\displaystyle \sin\theta\,=\,\frac{\sqrt{3}}{2}\,\text{ and }\,\tan\theta > 0.\;\;\text{ Find }\,\cos\theta.$
$\displaystyle \sin\theta$ is positive: .$\displaystyle \theta$ is in Quadrant 1 or Quadrant 2.
$\displaystyle \tan\theta$ is positive: .$\displaystyle \theta$ is in Quardrant 1 or Quadrant 3.
. . Hence, $\displaystyle \theta$ is in Quadrant 1.
$\displaystyle \sin\theta \:=\:\frac{\sqrt{3}}{2} \:=\:\frac{opp}{hyp}$
$\displaystyle \theta$ is in a right triangle with: .$\displaystyle opp = \sqrt{3},\;hyp = 2$
Pythagorus tell us that: .$\displaystyle adj = 1$
Therefore: .$\displaystyle \cos\theta \:=\:\frac{adj}{hyp} \:=\:\frac{1}{2}$
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.