If a runner is running uphill at an angle of \( 30^{\circ} \) at 8 miles per hour, what is her speed in the horizontal direction? (Round her speed to the nearest tenth.)

Given that \( \theta \) is an obtuse angle and \( \operatorname{cosec} \theta=k \), express, in terms of \( k \) (a) \( \cot \theta \)

0) Find the exact value of \( \tan \left(22.5^{\circ}\right) \).

(\$) Find the exact value of the followings using ceference ingles. (YOU SHOULD SHOW ME THE WAY TO USE REFERENCE ANGLES TO GET CREDITS.) \[ \sec \left(-\frac{4 \pi}{3}\right)=-\sec \left(60^{\circ}\right) \]

Verify the following: \[ (1-\cos (x))(\operatorname{cosec}(x)+\cot (x))=\sin (x) \]

A plane takes off at an angle of \( 11^{\circ} \) to the horizontal. If the plane maintains a speed of \( 270 \mathrm{~km} / \mathrm{h} \), what horizontal distance has it travelled after flying for 2 minutes?