Respuesta :
Answer:
a) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to [tex] 2\pi[/tex]:
[tex] 17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4[/tex]
For this case we know that [tex] sin (\pi/4) = \frac{\sqrt{2}}{2}[/tex]
So then [tex] sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}[/tex]
b) We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to [tex] 2\pi[/tex]:
[tex] 19 \pi/6 - 2\pi = \frac{7\pi}{6}[/tex]
For this case we know that [tex] cos (\pi/6) = \frac{\sqrt{3}}{2}[/tex]
And we know that [tex]\frac{7\pi}{6}[/tex] is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then [tex] cos(\frac{19 \pi}{6}) = -\frac{\sqrt{3}}{2}[/tex]
c) For this case that any factor of [tex] \pi[/tex] the sin function is equal to 0.
So from definition of tan we have this:
[tex] tan (450\pi) = \frac{sin(450 \pi)}{cos(450 \pi)}= \frac{0}{cos(450\pi)}= 0[/tex]
Step-by-step explanation:
a. sin (17pi / 4 )
We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to [tex] 2\pi[/tex]:
[tex] 17 \pi/4 - 2\pi = \frac{9\pi}{4} -2\pi = \pi/4[/tex]
For this case we know that [tex] sin (\pi/4) = \frac{\sqrt{2}}{2}[/tex]
So then [tex] sin(\frac{17 \pi}{4}) = \frac{\sqrt{2}}{2}[/tex]
b. cos (19pi / 6 )
We can remove the complete rotations around the unitary circle like this, because we know that one complete revolution is equivalent to [tex] 2\pi[/tex]:
[tex] 19 \pi/6 - 2\pi = \frac{7\pi}{6}[/tex]
For this case we know that [tex] cos (\pi/6) = \frac{\sqrt{3}}{2}[/tex]
And we know that [tex]\frac{7\pi}{6}[/tex] is on the III quadrant since is equivalent to 210 degrees. And on the III quadrant the cosine is negative. So then [tex] cos(\frac{19 \pi}{6}) = -\frac{\sqrt{3}}{2}[/tex]
c. tan(450pi)
For this case that any factor of [tex] \pi[/tex] the sin function is equal to 0.
So from definition of tan we have this:
[tex] tan (450\pi) = \frac{sin(450 \pi)}{cos(450 \pi)}= \frac{0}{cos(450\pi)}= 0[/tex]
