Question

Let theta equals 11 times pi over 12 periodPart A: Determine tan θ using the sum formula. Show all necessary work in the calculation.Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation.

Answer 1

The fisrt part is the divide your angle into two angles, could be 6/12π and 5/12π

$\begin{gathered} A=\frac{4\pi}{12}=\frac{\pi}{3} \\ B=\frac{7\pi}{12} \end{gathered}$

For the sum formula:

$\begin{gathered} \tan (\theta)=\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B} \\ \tan (A+B)=\frac{1.73-3.73}{1-1.73\cdot(-3.73)} \\ \tan (A+B)=\frac{-2}{7.45}=-0.27 \end{gathered}$

For the difference formula:

$\begin{gathered} A=\frac{1\pi}{12} \\ B=\pi \end{gathered}$$\begin{gathered} \tan (B-A)=\frac{\tan B-\tan A}{1+\tan A\cdot\tan B} \\ \tan (B-A)=\frac{0-0.268}{1+0\cdot0.267} \\ \tan (B-A)=-0.268 \end{gathered}$

Both methods work and result in the same answeer