12. Applications of Residues

Trigonometric Integrals — Quiz

Test your understanding of trigonometric integrals with 5 practice questions.

Practice Questions

Question 1

When $z=e^{it}$ is used to transform an integral over $t\in[0,2\pi]$, what contour does $z$ trace in the complex plane?

Question 2

If $z=e^{it}$, which formula correctly expresses $\cos t$ in terms of $z$?

Question 3

Under the substitution $z=e^{it}$, what is $dt$ in terms of $dz$?

Question 4

Evaluate $\int_0^{2\pi}\frac{dt}{2+\cos t}$.

Question 5

Evaluate $\int_0^{2\pi}\frac{\sin t}{3+\cos t}\,dt$.