Solution
Question 1.
[tex]\begin{gathered} \text{ since }\pi\text{ rad }=180^0 \\ \\ \Rightarrow65^0=\frac{65^0}{180^0}\pi\text{ rad} \\ \\ \Rightarrow65^0=\frac{13}{36}\text{ }\pi\text{ rad} \end{gathered}[/tex]
Question 2.
[tex]\begin{gathered} \text{ since }\pi\text{ rad }=180^0 \\ \\ \Rightarrow\frac{4}{5}\pi\text{ rad }=\frac{4}{5}\times180^0=144^0 \\ \\ \Rightarrow\frac{4}{5}\pi\text{ rad }=144^0 \end{gathered}[/tex]
Question 3.
Idea: The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis
For second quadrant, the corresponding angle is 180 - x => 180 - 81 = 99
For third quadrant, the corresponding angle is 180 + x => 180 + 81 = 261
For fourth quadrant, corresponding angle is 360 - x => 360 - 81 = 279
Hence, the other 3 parameters are, 99, 261, and 279
Question 4.
since 320 falls in the fourth quadrant, its reference angle is just 360 - 320 = 40
Therefore, its reference angle is 40 degrees.
