1.
The question requires you to find csc of angle thetha
The formula to apply is;

So, First find sin of the angle theta, then its reciprocal
Sin theta= opposite side length / hypotenuse
![\sin \emptyset=\frac{8}{8\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/veubv6zdopyqwcdatdd9pou6knuud8ohz4.png)


Answer
0.7071
Or
Using surds
![\sin \emptyset=\frac{8}{8\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/veubv6zdopyqwcdatdd9pou6knuud8ohz4.png)
Cancel 8 both in the denominator and numerator to remain with
![\sin \emptyset=\frac{1}{1\sqrt[]{2}}=\frac{1}{\sqrt[]{2}}](https://img.qammunity.org/2023/formulas/mathematics/college/xsnwi4oewgrye267pogr2vjosr07amyb2k.png)
T