Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

Answer: see below

Explanation:

`sin\ \theta=(y)/(r)=(84)/(85)\qquad \qquad \text{Quadrant I implies both x and y are positive}\\\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2+\ y^2=r^2\\x^2+84^2=85^2\\x^2\qquad =85^2-84^2\\x^2\qquad =169\\.\qquad x =13\\`

Input x = 13, y = 84, r = 85 into the trig functions:

`\sin\ \theta=(y)/(r)=\large\boxed{(84)/(85)}\qquad \qquad \qquad \csc \theta=(r)/(y)=\large\boxed{(85)/(84)}\\\\\\\\\cos\ \theta=(x)/(r)=\large\boxed{(13)/(85)}\qquad \qquad \qquad \sec \theta=(r)/(x)=\large\boxed{(85)/(13)}\\\\\\\\\tan\ \theta=(y)/(x)=\large\boxed{(84)/(13)}\qquad \qquad \qquad \cot \theta=(x)/(y)=\large\boxed{(13)/(84)}`