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  1. Sine and cosine from terminal side ●○○○○ 10 ptsThe terminal side of angle α\alpha lies on the ray y=−34xy = -\frac{3}{4}x with x>0x > 0. Find the value of 2sin⁡α+cos⁡α2\sin\alpha + \cos\alpha. Give your answer as a decimal.
  2. Difference of squared sine and cosine ●○○○○ 10 ptsEvaluate (sin⁡72∘+cos⁡18∘)(sin⁡72∘−cos⁡18∘)(\sin 72^\circ + \cos 18^\circ)(\sin 72^\circ - \cos 18^\circ).
  3. Sine minus cosine from a terminal point ●○○○○ 10 ptsThe terminal side of angle α\alpha passes through the point P(−2,4)P(-2,4). Find the value of sin⁡α−cos⁡α\sin\alpha - \cos\alpha. Round to two decimal places.
  4. Extrema of sine on an interval ●○○○○ 10 ptsFind the xx-values in [0,2π][0, 2\pi] at which f(x)=sin⁡xf(x)=\sin x attains its maximum and its minimum. Give each in degrees, with the maximum first and then the minimum.
  5. Sun's angle at latitude 42° ●○○○○ 10 ptsA building is located at latitude 42∘42^\circ. Using Angle of sun=90∘−latitude+(−23.5∘)⋅cos⁡[(N+10)⋅360∘365],\text{Angle of sun} = 90^\circ - \text{latitude} + (-23.5^\circ)\cdot\cos\left[(N+10)\cdot\frac{360^\circ}{365}\right], where NN is the day of the year, find the angle of inclination of the sun on March 10th, the 69th day of the year. Round to two decimal places.
  6. Abscissa from tangent of terminal side ●○○○○ 10 ptsThe terminal side of angle α\alpha passes through the point P(x,−6)P(x, -6), and tan⁡α=−35\tan\alpha = -\frac{3}{5}. Find the value of xx.
  7. Arcsine of sine of 10 ●●○○○ 20 ptsEvaluate sin⁡−1(sin⁡10)\sin^{-1}(\sin 10), where 1010 is in radians. Round your answer to two decimal places.
  8. Solutions of a trigonometric equation ●●○○○ 20 ptsFind the number of solutions to 1sin⁡2θ−1cos⁡2θ−1tan⁡2θ−1cot⁡2θ−1sec⁡2θ−1csc⁡2θ=−3\frac{1}{\sin^2 \theta} - \frac{1}{\cos^2 \theta} - \frac{1}{\tan^2 \theta} - \frac{1}{\cot^2 \theta} - \frac{1}{\sec^2 \theta} - \frac{1}{\csc^2 \theta} = -3 in the interval 0≤θ≤2π0 \le \theta \le 2\pi.
  9. Angle between y = x² and y = 1/x ●●○○○ 20 ptsFind the acute angle of intersection, in degrees, between the curves y=x2y = x^2 and y=1xy = \dfrac{1}{x}, measured between their tangents at the point of intersection. Round to two decimal places.
  10. Cosine of arcsecant plus arccosecant ●●○○○ 20 ptsEvaluate cos⁡(sec⁡−1x+csc⁡−1x)\cos\left(\sec^{-1}x+\csc^{-1}x\right) for ∣x∣≥1|x|\geq 1. (The answer is a single number, the same for every such xx.)

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