Answer: 14/15
This is because to get to 14/15 you must divide by 6 but when getting to 42/45 you must divide 2. Therefore 14/15 is your answer because the problem went to the most reduced fraction.
lol
Step-by-step explanation:
Answer:Yes
Step-by-step explanation:
well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.
![\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}](https://tex.z-dn.net/?f=%5Cbf%20sin%5E2%28%5Ctheta%29%2Bcos%5E2%28%5Ctheta%29%3D1~%5Chspace%7B10em%7D%20tan%28%5Ctheta%20%29%3D%5Ccfrac%7Bsin%28%5Ctheta%20%29%7D%7Bcos%28%5Ctheta%20%29%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20sin%5E2%28a%29%2Bcos%5E2%28a%29%3D1%5Cimplies%20cos%5E2%28a%29%20%3D%201-sin%5E2%28a%29%20%5C%5C%5C%5C%5C%5C%20cos%5E2%28a%29%20%3D%201-%5Bsin%28a%29%5D%5E2%5Cimplies%20cos%5E2%28a%29%20%3D%201-%5Cleft%28%20%5Ccfrac%7B3%7D%7B4%7D%20%5Cright%29%5E2%5Cimplies%20cos%5E2%28a%29%20%3D%201-%5Ccfrac%7B3%5E2%7D%7B4%5E2%7D%20%5C%5C%5C%5C%5C%5C%20cos%5E2%28a%29%20%3D%201-%5Ccfrac%7B9%7D%7B16%7D%5Cimplies%20cos%5E2%28a%29%20%3D%20%5Ccfrac%7B7%7D%7B16%7D%5Cimplies%20cos%28a%29%3D%5Cpm%5Csqrt%7B%5Ccfrac%7B7%7D%7B16%7D%7D)
![\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}](https://tex.z-dn.net/?f=%5Cbf%20cos%28a%29%3D%5Cpm%5Ccfrac%7B%5Csqrt%7B7%7D%7D%7B%5Csqrt%7B16%7D%7D%5Cimplies%20cos%28a%29%3D%5Cpm%5Ccfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bon%20the%20II%20Quadrant%7D%7D%7Bcos%28a%29%3D-%5Ccfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D%7D%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5Ctan%28a%29%3D%5Ccfrac%7Bsin%28a%29%7D%7Bcos%28a%29%7D%5Cimplies%20tan%28a%29%3D%5Ccfrac%7B~~%5Cfrac%7B3%7D%7B4%7D~~%7D%7B-%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D%7D%5Cimplies%20tan%28a%29%3D%5Ccfrac%7B3%7D%7B4%7D%5Ccdot%20%5Ccfrac%7B4%7D%7B-%5Csqrt%7B7%7D%7D%5C%5C%5C%5C%5C%5Ctan%28a%29%3D-%5Ccfrac%7B3%7D%7B%5Csqrt%7B7%7D%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7Btan%28a%29%20%3D%20-1.13%7D)