Answer:
Step-by-step explanation:
Alright, lets get started.
You my refer the unit circle I have attached.
1) [tex]sin \frac{17 \pi }{6}[/tex]
We have to find exact value of this.
Usually, we could refer the unit circle and find the corresponding sin value of that angle but in this, angle [tex]\frac{17 \pi }{6}[/tex] is not on unit circle as it is more than 2[tex]\pi[/tex].
So, first we will find co-terminal angle of [tex]\frac{17 \pi }{6}[/tex] by subtracting 2[tex]\pi[/tex] from it.
So, its co-terminal angle is : [tex]\frac{17 \pi }{6} - 2\pi = \frac{17 \pi }{6}-\frac{12 \pi }{6}[/tex]
So, co-terminal angle will be = [tex]\frac{5\pi }{6}[/tex]
So, referring unit circle,
[tex]sin (\frac{5\pi }{6} )= \frac{1}{2}[/tex] : Answer
2) [tex]tan(\frac{13\pi }{4} )[/tex]
Finding co-terminal :
[tex]\frac{13\pi }{4}-2\pi=\frac{13\pi }{4} -\frac{8\pi }{4}=\frac{5\pi }{4}[/tex]
So, referring unit circle,
[tex]tan(\frac{5\pi }{4} )=1[/tex] : Answer
3) [tex]sec(\frac{11\pi }{3} )[/tex]
Finding co-terminal:
[tex]\frac{11\pi }{3}-2\pi=\frac{11\pi }{3}-\frac{6\pi }{3}=\frac{5\pi }{3}[/tex]
[tex]cos(\frac{5\pi }{3} )=\frac{1}{2}[/tex]
Se we know, sec is reciprocal of cos, so we will flip the value of cos to find sec.
[tex]sec(\frac{5\pi }{3} )= 2[/tex] : Answer
