May 2017

Find $\displaystyle \sum_{n = 1}^5 S_n$ where $S_n = 2/n$.

Find the 6^th term of $1, ~ 2, ~ 5, ~ ... \, , ~ \frac{1}{2}(1 + 3^{n - 1})$.

Find the 8^th term of the sequence $-3, ~ 4, ~ 5/3, ~ … \, , ~ \dfrac{n + 2}{2n - 3}$.

In the figure, $\varphi$ represents the angle subtended by a 5 ft picture when viewed from point P that is 7 ft below the picture and 14 ft away from the wall on which the picture hangs. Solve for $\varphi$ and express the answer using the arctan notation.

Solve for x if $\arcsin (x + 2) = \pi/6$.

Find the exact value of $\arccos (\tan 45^\circ)$.

Evaluate the $\tan (\arctan 3 + \arctan 4)$.

Evaluate the $\tan (\arctan 3 - \arctan 2)$.

Find the exact value of $\cos [ \, \arcsin (2/3) \, ]$.

At a point A that is 50 m from the base of a monument, the angle of elevation to the top of the monument is twice as large as the angle of elevation from a point B that is 150 m from the monument. Assuming that the base of the monument and the points A and B are in the same line on level ground, find the height of the monument.