Question 1

Find the value of $ \sec\left( \arctan\left( \frac{15} {8}\right)\right)$

Accepted Answer

$\frac{17}{8}$

Answer

$-\frac{17}{8}$

Answer

$\frac{17}{15}$

Answer

-$\frac{8}{15}$

Question 2

If $\angle{A}$ lies in quadrant 2 with $\sin(A)=\frac{5}{13}$ and  $\angle{B}$ lies in quadrant 3 with $	an(B)=\frac{4}{3}$, find $\cos(A + B)$.

Accepted Answer

$\frac{56}{65}$

Answer

$\frac{63}{65}$

Answer

$\frac{33}{65}$

Answer

$\frac{16}{65}$

Question 3

$	ext{In } 	riangle ABC, a=7,b=15,	ext{and m}\angle A=26\degree.$ Find all possible m$\angle B$ to the nearest degree.

Accepted Answer

$70\degree$ and $110\degree$

Answer

$70\degree$

Answer

$12\degree$ and $168\degree$

Answer

$12\degree$

Question 4

Find all possible values that satisfy the equation $2\cos^2{(x)}-\cos{(x)}-1=0$ over the interval $0\degree \leq x < 360\degree$.

Accepted Answer

$0\degree, 120\degree,240\degree$

Answer

$60\degree, 180\degree,240\degree$

Answer

$0\degree, 60\degree,300\degree$

Answer

$120\degree, 180\degree,240\degree$

Question 5

For $y=-210 \csc{(10x - 30\pi)}$, identify the amplitude, period, and phase shift.

Question 6

Two forces act on an object at an angle of $31\degree$. The larger force is 21 Newtons and the smaller force is 14 N. Find the resultant force to the nearest Newton.

Accepted Answer

34 Newtons

Answer

1141 Newtons

Answer

18 Newtons

Answer

334 Newtons

Question 7

Solve for x:$ 2\cos^2{(x)}-5\cos{(x)}=3, [0,2\pi)$

Accepted Answer

$\frac{2\pi}{3},\frac{4\pi}{3}$

Answer

$\pi$

Answer

$0$

Answer

$\frac{\pi}{3},\frac{5\pi}{3}$

Question 8

State the exact value of $\cos{(15\degree)}$.

Accepted Answer

$\frac{1+\sqrt{3}}{2\sqrt{2}}$

Answer

$\frac{1-\sqrt{3}}{2\sqrt{2}}$

Answer

$\frac{-1+\sqrt{3}}{2\sqrt{2}}$

Answer

$\frac{-1-\sqrt{3}}{2\sqrt{2}}$

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