CSC Events

Unizor – Trigonometry – CSC of All Basic Angles

Before solving these problems review the graph and basic properties of a function csc(x):
1. Is it odd, even, periodical or neither?
2. What kind of symmetry, if any, does its graph have?
3. Does it equal to zero at some points and, if it does, where?
4. Does it have asymptotes and, if does, where?
5. What are its maximum and minimums and at what values of an argument?
6. What are its values for basic angles in the first quadrant (0, π/6, π/4, π/3, π/2)?
7. How the value of a function changes if we change the argument by π or −π?

After answering all these questions calculate the values below and only then watch the video.

(a) csc(2π/3)
(b) csc(3π/4)
(c) csc(5π/6)
(d) csc(π)
(e) csc(−π/6)
(f) csc(−π/4)
(g) csc(−π/3)
(h) csc(−π/2)
(i) csc(−2π/3)
(j) csc(−3π/4)
(k) csc(−5π/6)
(l) csc(−π)

Answers:
(a) 2√3/3; (b) √2; (c) 2;
(d) Undef; (e) −2; (f) −√2;
(g) −2√3/3; (h) −1; (i) −2√3/3;
(j) −√2; (k) −2; (l) Undef.