Refer to the right triangle in the figure. Click on the picture to see it more clearly.

If , \(BC=5\) and the angle \(\beta=65 ^\circ\text{,}\) find any missing angles or sides. Give your answer to at least 3 decimal digits.

AB =

AC =

\(\alpha\)=

8.

Click on the graph to view a larger graph

For the given angle \(x\) in the triangle given in the graph

\(\sin x=\) ;

\(\cos x=\) ;

\(\tan x=\) ;

\(\cot x=\) ;

\(\sec x=\) ;

\(\csc x=\) ;

9.

Solve the following equations in the interval [0,2\(\pi\)].

Note: Give the answer as a multiple of \(\pi\text{.}\) Do not use decimal numbers. The answer should be a fraction or an integer. Note that \(\pi\) is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is \(\pi/2\) you should enter 1/2. If there is more than one answer enter them separated by commas.

\(\sin(t)= -\frac{1}{2}\)

\(t=\)\(\pi\)

\(\sin(t)= \frac{\sqrt{2}}{2}\)

\(t=\)\(\pi\)

10.

Solve the following equations in the interval [0, 2 \(\pi\)].

Note: Give the answer as a multiple of \(\pi\text{.}\) Do not use decimal numbers. The answer should be a fraction or an integer. Note that \(\pi\) is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is \(\pi/2\) you should enter 1/2. If there is more than one answer enter them separated by commas.