Answer:
Part 1)
![cos(\theta)=-(60)/(61)](https://img.qammunity.org/2020/formulas/mathematics/college/s2xqe11hzsoahdzm30piz1s52cwyqnswgc.png)
Part 2)
Part 3)
Part 4)
Part 5)
Explanation:
we know that
If angle theta lie on Quadrant III
then
The function sine is negative
The function cosine is negative
The function tangent is positive
The function cotangent is positive
The function cosecant is negative
The function secant is negative
step 1
Find
we know that
![cos(\theta)=(1)/(sec(\theta))](https://img.qammunity.org/2020/formulas/mathematics/high-school/bs0xumnqg19l0alzk7heriarvmo11nso5h.png)
we have
----> the value must be negative
therefore
![cos(\theta)=-(60)/(61)](https://img.qammunity.org/2020/formulas/mathematics/college/s2xqe11hzsoahdzm30piz1s52cwyqnswgc.png)
step 2
Find
![tan(\theta)](https://img.qammunity.org/2020/formulas/mathematics/high-school/1fzm3lbiukiniqba38q1irnfwo2wjxg1ib.png)
we know that
we have
substitute
step 3
Find
![cot(\theta)](https://img.qammunity.org/2020/formulas/mathematics/college/bks19t26b5uvvnfx43096ynpsx7owcpimi.png)
we know that
![cot(\theta)=(1)/(tan(\theta))](https://img.qammunity.org/2020/formulas/mathematics/college/e1rx5lpmsd708pgwvc1tw8c5cirj73jvya.png)
we have
therefore
step 4
Find
![csc(\theta)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4chswh0vqqt5c4fyxy99ojht5fuxsdyqvj.png)
we know that
![cot^(2) (\theta)+1=csc^(2) (\theta)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yjwillmcy9f1r3jaor4i5nfwjt9ljylkjm.png)
we have
substitute
![((60)/(11))^(2)+1=csc^(2) (\theta)](https://img.qammunity.org/2020/formulas/mathematics/college/7llc1g0fylo73iagnx6ukq6wzcedee0d6u.png)
![(3,600)/(121)+1=csc^(2) (\theta)](https://img.qammunity.org/2020/formulas/mathematics/college/4dv8ffipo5oyl3p1owsvddb0ejio5l5lfh.png)
![(3,721)/(121)=csc^(2) (\theta)](https://img.qammunity.org/2020/formulas/mathematics/college/epok12b1ii0daebueoj9my42k4pyn5m7i6.png)
square root both sides
![csc(\theta)=-(61)/(11)](https://img.qammunity.org/2020/formulas/mathematics/college/5541c5rsqd24te63cnck5cysqsaue594ds.png)
step 5
Find
![sin(\theta)](https://img.qammunity.org/2020/formulas/mathematics/high-school/fb7gus8q4puq8tqwmhu13r1e7cljlc9mca.png)
we know that
![sin(\theta)=(1)/(csc(\theta))](https://img.qammunity.org/2020/formulas/mathematics/college/le40bayd2bpi66zkpnisligpjhai5ofvek.png)
we have
![csc(\theta)=-(61)/(11)](https://img.qammunity.org/2020/formulas/mathematics/college/5541c5rsqd24te63cnck5cysqsaue594ds.png)
therefore
![sin(\theta)=-(11)/(61)](https://img.qammunity.org/2020/formulas/mathematics/college/59f0puc3tkfqqvj7vo3g24vm7fa8paf65s.png)