Q1) $\tan \theta + \cot \theta =$

A. $2\tan \theta$

B. $2 \cot \theta$

C. $2 \sec \theta$

D. $\dfrac{1}{\dfrac{1}{2} \sin(2\theta)}$

E. $\dfrac{1}{\sin(2\theta)}$

Q2) If $\sin \beta = \dfrac{1}{7}$ and $\beta$ is in quadrant II, then $\cos \beta =$

A. $\dfrac{4\sqrt 3}{7}$

B. $-\dfrac{4\sqrt 3}{7}$

C. $\dfrac{6}{7}$

D. $-\dfrac{6}{7}$

E. $\dfrac{48}{49}$

Q3) If $\cos \alpha = \dfrac{1}{3}$ and $0 < \alpha< \pi$, then $cos (\dfrac {\alpha}{2}) = $

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

B. $-\dfrac{1}{6}$

C. $\dfrac{1}{6}$

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

E. $\dfrac{2}{3}$

Q4) $x$ in terms of $y$ in the right triangle below could be written as follows

A. $x=10-y$

B. $x=\sqrt{100-y}$

C. $x=\sqrt{100+y^2}$

D. $x=\sqrt{100+y}$

E. $x=\sqrt{100-y^2}$

Q5) Which is the graph of $y=\sin (-x)$

A.  

B.  

C.  

D.  

E.  

Q6) What is the maximum value of $y$ if $y=2−2\sin(2x)$ and $x$ varies from $0$ to $4\pi$?

A. $2$

B. $0$

C. $4$

D. $8$

E. $6$

Q7) If $\sin(x)=−0.2$, then $\sin(x+1000\pi)=$

A. $0.2$

B. $1000$

C. $-0.2$

D. $200$

E. $-200$

Q8) Convert $25^\circ$ to radians

A. $\dfrac{36 \pi}{5}$

B. $\dfrac{5 \pi}{36}$

C. $\dfrac{36}{5\pi}$

D. $\dfrac{5}{36\pi}$

E. $\dfrac{\pi}{36}$

A. $\dfrac{1}{\sqrt 2} \sin x$

B. $\dfrac{1}{\sqrt 2}cos x$

C. $\dfrac{1}{\sqrt 2} (\cos x + \sin x)$

D. $\cos x + \sin x$

E. $\dfrac{1}{\sqrt 2} (\cos x - \sin x)$

Q10) $\cos (75^\circ) = $

A. $\dfrac{\sqrt 6 + \sqrt 2}{4}$

B. $\dfrac{\sqrt 6 - \sqrt 2}{4}$

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

D. $\dfrac{-\sqrt 6 - \sqrt 2}{4}$

E. $\dfrac{-\sqrt 6 + \sqrt 2}{4}$