(a) Find an angle between 0° and 360° that is coterminal with – 120°.(b) Find an angle between 0 and 2π that is coterminal with 15π/4Give exact values for your answers.
Accepted Solution
A:
Answer:a) [tex]240\degree[/tex]b) [tex]\frac{15\pi}{4}[/tex]Step-by-step explanation:Coterminal angles have the same terminal sides in standard position.a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range. [tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive. b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]