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5 problems match “sine and cosine”. Clear

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1. Sine and cosine from terminal side ●○○○○ 10 ptsThe terminal side of angle $\alpha$ lies on the ray $y = -\frac{3}{4}x$ with $x > 0$. Find the value of $2\sin\alpha + \cos\alpha$. Give your answer as a decimal.
2. Difference of squared sine and cosine ●○○○○ 10 ptsEvaluate $(\sin 72^\circ + \cos 18^\circ)(\sin 72^\circ - \cos 18^\circ)$.
3. Double-angle sine from given sine and cosine ●○○○○ 10 ptsIf $\theta$ is an angle in the first quadrant with $\sin(\theta) = \frac{3}{5}$ and $\cos(\theta) = \frac{4}{5}$, find $\sin(2\theta)$. Give your answer as a decimal.
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. Sum of x and y in a system ●●●○○ 50 ptsGiven that $x+\sin y=2008$ and $x+2008 \cos y=2007$, where $0 \leq y \leq \frac{\pi}{2}$, find the value of $x+y$. Give your answer as a decimal rounded to two decimal places.