Answers:
a) 0.86
b) -0.86
c) -1.73
d) 0.86
Step-by-step explanation:
We are told [tex]cos \theta=-\frac{1}{2}[/tex]. So, we first have to find the value of [tex]\theta[/tex] which is an obtuse angle (an angle greater than [tex]90\°[/tex] and smaller than [tex]180\°[/tex]):
[tex]\theta=cos^{-1} (-\frac{1}{2})[/tex]
[tex]\theta=120\°[/tex]
Now that we know the value of the angle [tex]\theta[/tex], let's begin with the answers:
a) [tex]sin \theta=sin (120\°)=0.86[/tex]
b) [tex]sin 2\theta=sin (2(120\°)=sin (240\°)=-0.86[/tex]
c) [tex]tan \theta=tan (120\°)=-1.73[/tex]
d) [tex]tan 4\theta=sin (4(120\°)=sin (480\°)=0.86[/tex]
