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5 problems match “special angles”. Clear

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1. Inclination angle of a vertical line ●○○○○ 10 ptsThe line $l$ is given by $x = \tan\left(-\frac{\pi}{6}\right)$. Find the inclination angle of $l$ in degrees.
2. Sum of inverse cosine and sine ●○○○○ 10 ptsFind the value of $\cos^{-1}\left(\frac{1}{2}\right) + 2\sin^{-1}\left(\frac{1}{2}\right)$. Give your answer in degrees.
3. Inclination angle from a direction vector ●○○○○ 10 ptsThe direction vector of the line $l$ has coordinates $(2, 2\sqrt{3})$. Find the inclination angle of the line $l$ in degrees, where the angle lies in $[0^\circ, 180^\circ)$.
4. Ratio of sine and cosine differences ●●○○○ 20 ptsEvaluate $\frac{\sin 35^{\circ} -\sin 25^{\circ}}{\cos 35^{\circ} -\cos 25^{\circ}}$. Round to two decimal places.
5. Maximum of x+y under a trig constraint ●●○○○ 20 ptsFind the maximum value of $x+y$ if $(2\sin x-1)(2\cos y-\sqrt{3})=0$, $x\in[0,3\pi/2]$, $y\in[\pi,2\pi]$. Round to two decimal places.