First, determine the quadrant for \( \theta \) ; then find \( x , y \) , and \( r \) ; and finally, give all six trigonometric ratios for \( \theta \) given the following information: \(\sin ( \theta ) = - \frac { 9 } { 19 } \) and \( \cos ( \theta ) < 0\) \(\theta \) lives in quadrant- \(x = \) - \(y = \) - \(r= \)1. \(\sin ( \theta ) = \) 2. \(\cos ( \theta ) = \) 3. \(\tan ( \theta ) = \) 4. \(\sec ( \theta ) = \) 5. \(\csc ( \theta ) = \) 6. \(\cot ( \theta ) = \) 

\[ \cos 9 x \cdot \cos ^{3} x-\sin 9 x \cdot \sin 3 x=\sin 4 x \] denkleminin en küçük pozitif kökü kaç derecedir? \( \underbrace{\text { A) } 6} \) \( \begin{array}{llll}\text { B) } 8 & \text { C) } 9 & \text { D) } 10 & \text { E) } 12\end{array} \)

What is the relationship between the hypotenuse and the adjacent side when defining secant?

If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator.

Drow the graph of \( J=\tan \left(2 x+90^{\circ}\right) \) for \( x \in\left[-90^{\circ} ; 90^{\circ}\right. \)

If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m i^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator