Q1) Which of the following graphs corresponds to the graph of $y = \sin x \cos x$

A.

B.

C.

D.

E.

Q2) If $A$ and $B$ are angles in quadrant I and $\sin A = \dfrac{1}{5}$ and $\sin B = \dfrac{1}{4}$, then $\sin(A+B)=$

A. $\dfrac{9}{20}$

B. $-\dfrac{\sqrt 15 + 2\sqrt 6}{20}$

C. $\dfrac{\sqrt 15 + 2\sqrt 6}{20}$

D. $\dfrac{1}{20}$

E. $\dfrac{\sqrt 15 - 2\sqrt 6}{20}$

Q3) $\sin(2x)+\cos (2x) + 2\sin ^2 x$ is equivalent to

A. $2\sin(x)\cos(x)$

B. $2\sin(x)\cos (x)-\sin ^2x + 1$

C. $2\sin (2x+\dfrac{\pi}{4})$

D. $2\sin (2x-\dfrac{\pi}{4})$

E. $2\sin(x)\sin(x) + 1$

Q4) What is the exact value of $\sin (2x)$ if $\sin x = \dfrac{1}{5}$ and $x$ is in quadrant $I$?

A. $\dfrac{8}{25}$

B. $\dfrac{2}{5}$

C. $\dfrac {-1}{5}$

D. $\dfrac{4 \sqrt 6}{25}$

E. $\dfrac {2 \sqrt 6}{5}$

Q5) Over which of the following intervals is $\cos x \lt \sin x$?

A.   $(0 , \dfrac{\pi}{4})$

B.   $(\dfrac{\pi}{4}, \dfrac{5\pi}{4})$

C.   $(\dfrac{5\pi}{4} , \dfrac{3\pi}{2})$

D.   $(\dfrac{3\pi}{2} , \dfrac{7\pi}{4})$

E.   $(\dfrac{7\pi}{4} , 2\pi)$

Q6) If $f(\theta)=sin(2\theta+\dfrac{\pi}{2})$ and $h(\theta)=\tan(\theta + \dfrac{3\pi}{4})$, then $f(h(\dfrac{\pi}{4}))=$

A. $0$

B. $1$

C. $-1$

D. $\dfrac{1}{2}$

E. $-\dfrac{1}{2}$

Q7) What is the solution set for the equation $-\sin ^2 x=-2(\cos x+1)$ for $0 \lt x \lt 2\pi$ ?

A. $\{\pi \}$

B. $\{0, \pi \}$

C. $\{0, \pi , 2\pi \}$

D. $\{0, \dfrac{\pi}{2} , 2\pi \}$

E. $\{\dfrac{\pi}{2} , 2\pi \}$

Q8) Which function corresponds to the graph shown below?

A. $y=\dfrac{1}{2}cos(4x)$

B. $y=-\dfrac{1}{2}cos(x)$

C. $y=\dfrac{1}{2}sin(4x)$

D. $y=-\dfrac{1}{2}sin(4x+\pi/2)$

E. $y=-\dfrac{1}{2}cos(4x+\pi)$

A. $\dfrac{3}{\sqrt {13}}$

B. $\dfrac{2}{\sqrt {13}}$

C. $\dfrac{1}{\sqrt {3}}$

D. $\dfrac{2}{\sqrt {3}}$

E. $\dfrac{1}{5}$

Q10) What is $\cos x$ if $-3 \cos(-x) + 4 = 5$?

A. $\dfrac{1}{3}$

B. $1$

C. $-\dfrac{1}{3}$

D. $-1$

E. $0$