Cards In This Deck

• $\text{First step to solve a bearing problem involving trigonometry?}$
  $\text{Draw a clear diagram with North lines at every point.}$
• $\text{Write the Sine Rule for finding a side length.}$
  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
• $$\begin{gathered} \text{True or False?} \\ \text{If calculating an angle using the Sine Rule, there is always only one possible answer.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: There could be two (Ambiguous Case).} \end{gathered}$$
• $\text{When using the Cosine Rule to find an angle, which formula should you start with?}$
  $\cos A=\frac{b^2+c^2-a^2}{2bc}$
• $\text{To find the angle in a triangle with sides 5, 6, and 7, which rule must you use?}$
  $\text{Cosine Rule (SSS case).}$
• $\text{When solving a triangle, if you know two sides and the included angle (SAS), which rule do you use first?}$
  $\text{Cosine Rule}$
• $\text{For the area formula }Area=\frac{1}{2}ab\sin C\text{, what condition must angle }C\text{ satisfy?}$
  $\text{It must be the included angle between sides }a\text{ and }b\text{.}$
• $\text{When finding the area of a segment (shaded region cut by a chord), which two areas do you subtract?}$
  $\text{Area of Sector - Area of Triangle}$
• $\text{Write the conversion factor to change degrees to radians.}$
  $$\begin{gathered} \times \frac{ \\ \pi }{180} \end{gathered}$$
• $$\begin{gathered} \text{First step to solve }2\theta +1.5= \\ \pi \text{ for an angle in a circle sector problem?} \end{gathered}$$
  $$\begin{gathered} \text{Rearrange to find }\theta \text{: }\theta =\frac{ \\ \pi -1.5}{2}\text{.} \end{gathered}$$
• $$\begin{gathered} \text{Which of these is 3 radians?} \\ \text{1. Slightly less than }180^{\circ } \\ \text{2. Exactly }180^{\circ } \\ \text{3. Slightly more than }180^{\circ } \end{gathered}$$
  $\text{1. Slightly less than }180^{\circ }$
• $\text{To find the perimeter of a sector, what must you add to the arc length?}$
  $\text{Two radii (}2r\text{).}$
• $$\begin{gathered} \text{Write the exact value of }\cos (\frac{ \\ \pi }{3})\text{.} \end{gathered}$$
  $\frac{1}{2}$
• $$\begin{gathered} \text{True or False?} \\ \text{An angle of }270^{\circ }\text{ is equal to }\frac{2 \\ \pi }{3}\text{ radians.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }\frac{3 \\ \pi }{2}\text{ radians} \end{gathered}$$
• $\text{Write the formula for arc length }l\text{ in a circle of radius }r\text{ and angle }\theta \text{ radians.}$
  $l=r\theta$
• $$\begin{gathered} \text{True or False?} \\ \text{The area of a sector with radius }r\text{ and angle }\theta \text{ radians is }A= \\ \pi r^2\theta \text{.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }A=\frac{1}{2}{r}^2\theta \end{gathered}$$
• $\text{Condition required to use the formula }A=\frac{1}{2}{r}^2(\theta -\sin \theta )\text{?}$
  $\theta \text{ must be in radians.}$