Here, we have to find the values of all these trigonometric ratios.
a)cos210∘
Now, 210∘ can be written as: 210∘=270∘−60∘ and it lies in the first quadrant, where cos of any angle is negative.
⇒cos210∘=cos(270∘−60∘)=−sin60∘
⇒cos210∘=−sin60∘=−√32
b)sin135∘
Now, 135∘ can be written as: 135∘=90∘+45∘ and it lies in the second quadrant, where sin of any angle is positive.
⇒sin135∘=sin(90∘+45∘)=cos45∘
⇒sin135∘=cos45∘=1√2
c)tan17π6
Now, 17π6 can be written as: 17π6=5π2+π3 and it lies in the second quadrant, where tan of any angle is negative.
⇒tan17π6=tan(5π2+π3)=−cotπ3
⇒tan17π6=−cotπ3=−1√3
d)cos23π3
Now, 23π3 can be written as: 23π3=7π2+π3 and it lies in the fourth quadrant, where cos of any angle is positive.
⇒cos23π3=cos(7π2+π3)=sinπ3
⇒cos23π3=sinπ3=√32