Trigonometry in context Quiz

1. A model $T=15+8\cos\left(\frac{\pi t}{12}\right)$, $t$ in hours. What is the period?

• A. $12$ hours
• B. $8$ hours
• C. $24$ hours
• D. $\frac{\pi}{12}$ hours

2. What is the least value of $9+4\sin(2t)$?

• A. $13$
• B. $9$
• C. $-4$
• D. $5$

3. A force of $10$ N acts at $30^\circ$ above the horizontal. What is its vertical component?

• A. $5$ N
• B. $10\cos30^\circ$ N
• C. $\frac{10}{\sin30^\circ}$ N
• D. $10$ N

4. For $D=12+4\sin(\cdots)$, on what fraction of the cycle is $D>12$?

• A. $\frac14$
• B. $\frac12$
• C. $\frac13$
• D. $\frac23$

5. A projectile with $u=15\ \text{m s}^{-1}$ lands $\frac{225}{2g}$ m away. What is a possible launch angle?

• A. $45^\circ$
• B. $60^\circ$
• C. $30^\circ$
• D. $15^\circ$