Answer:
5/6
Step-by-step explanation:
1 4/6-5/6=?
1 4/6=10/6
10/6-5/6=5/6
Answer:
there are 25 students in the class and 15 who wear glasses.
Yes it is the answer that is last on the list because it is that answer
Answer:
After 'n' weeks?
Step-by-step explanation:
Make sure your question makes sense.
If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701_______________
![\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\ \mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\ \mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}](https://tex.z-dn.net/?f=%5Cmathsf%7Btan%5C%2C%5Ctheta%3D%5Cdfrac%7B1%7D%7B4%7D%5Cqquad%5Cqquad%28sin%5C%2C%5Ctheta%5C%20%5Ctextgreater%20%5C%200%29%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2C%5Ctheta%7D%7Bcos%5C%2C%5Ctheta%7D%3D%5Cdfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7B4%5C%2Csin%5C%2C%5Ctheta%3Dcos%5C%2C%5Ctheta%5Cqquad%5Cquad%28i%29%7D)
Square both sides:
![\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\ \mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\ \mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\ \mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}](https://tex.z-dn.net/?f=%5Cmathsf%7B%284%5C%2Csin%5C%2C%5Ctheta%29%5E2%3D%28cos%5C%2C%5Ctheta%29%5E2%7D%5C%5C%5C%5C%0A%5Cmathsf%7B4%5E2%5C%2Csin%5E2%5C%2C%5Ctheta%3Dcos%5E2%5C%2C%5Ctheta%7D%5C%5C%5C%5C%0A%5Cmathsf%7B16%5C%2Csin%5E2%5C%2C%5Ctheta%3Dcos%5E2%5C%2C%5Ctheta%5Cqquad%5Cqquad%28but%2C~cos%5E2%5C%2C%5Ctheta%3D1-sin%5E2%5C%2C%5Ctheta%29%7D%5C%5C%5C%5C%0A%5Cmathsf%7B16%5C%2Csin%5E2%5C%2C%5Ctheta%3D1-sin%5E2%5C%2C%5Ctheta%7D)
![\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\ \mathsf{17\,sin^2\,\theta=1}\\\\ \mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\ \mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\ \mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}](https://tex.z-dn.net/?f=%5Cmathsf%7B16%5C%2Csin%5E2%5C%2C%5Ctheta%2Bsin%5E2%5C%2C%5Ctheta%3D1%7D%5C%5C%5C%5C%0A%5Cmathsf%7B17%5C%2Csin%5E2%5C%2C%5Ctheta%3D1%7D%5C%5C%5C%5C%0A%5Cmathsf%7Bsin%5E2%5C%2C%5Ctheta%3D%5Cdfrac%7B1%7D%7B17%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cpm%5C%2C%5Csqrt%7B%5Cdfrac%7B1%7D%7B17%7D%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cpm%5C%2C%5Cdfrac%7B1%7D%7B%5Csqrt%7B17%7D%7D%7D)
Since
![\mathsf{sin\,\theta}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%7D)
is positive, you can discard the negative sign. So,
![\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7B17%7D%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
Substitute this value back into
![\mathsf{(i)}](https://tex.z-dn.net/?f=%5Cmathsf%7B%28i%29%7D)
to find
![\mathsf{cos\,\theta:}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3A%7D)
![\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7B4%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Csqrt%7B17%7D%7D%3Dcos%5C%2C%5Ctheta%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B%5Csqrt%7B17%7D%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus</em>