Answer:
Step-by-step explanation:
First, anwsering our last question, you can break it down using radians or degrees, it doesn't matter because they represent the same quantities. For this type of exercise, the most common is radians.
When we are breaking the angles, it is easier if we could find the primary angles ( π/6 , π/4, π/3 , π/2 and π). So, this is what I'm gonna do:
[tex]\frac{17\pi}{12} = \frac{12\pi}{12} + \frac{5\pi}{12} = \pi + \frac{5\pi}{12}[/tex]
Okay, but now we have this [tex]\frac{5\pi}{12}[/tex] on the way. Sometimes is difficult to understand the measure of the angle when it is in radians, so I prefer to convert to degrees
[tex]\frac{5\pi}{12}[/tex] = 5 × 180 / 12 = 900/ 12 = 75°
Now it's way easier to realise that 75° can be decomposed as 45° + 30°,
or [tex]\frac{\pi}{4} + \frac{\pi}{6}[/tex] .
Then, to solve the first problem, we need to split the solvinf into 2 steps:
- step 1 ⇒ sin( [tex]\pi + \frac{5\pi}{12}[/tex] ) = sin ([tex]\pi[/tex]) + sin ([tex]\frac{5\pi}{12}[/tex])
- step 2 ⇒ sin ([tex]\frac{5\pi}{12}[/tex]) = sin ([tex]\frac{\pi}{4} + \frac{\pi}{6}[/tex] ) = sin ([tex]\frac{\pi}{4}[/tex]) + sin ([tex]\frac{\pi}{6}[/tex])
Note you will have to find sin ([tex]\frac{5\pi}{12}[/tex]) first to be able to finish the step 1.
I hope I could help you :)
