Question

from the information given, find the quadrant in which the terminal point determined by t lies. input i, ii, iii, or iv. (a) \\( \sin ( t ) < 0 \\) and \\( \cos ( t ) < 0 \\), quadrant (b) \\( \sin ( t ) > 0 \\) and \\( \cos ( t ) < 0 \\), quadrant (c) \\( \sin ( t ) > 0 \\) and \\( \cos ( t ) > 0 \\), quadrant (d) \\( \sin ( t ) < 0 \\) and \\( \cos ( t ) > 0 \\), quadrant question help: worked example 1

Explanation:

Step1: Recall the signs of sine and cosine in each quadrant

• In Quadrant I: \(\sin(t)>0\) and \(\cos(t)>0\)
• In Quadrant II: \(\sin(t)>0\) and \(\cos(t)<0\)
• In Quadrant III: \(\sin(t)<0\) and \(\cos(t)<0\)
• In Quadrant IV: \(\sin(t)<0\) and \(\cos(t)>0\)

Step2: Match the given conditions to the quadrants

• (a) For \(\sin(t)<0\) and \(\cos(t)<0\), using the above rules, the terminal point lies in Quadrant III.
• (b) For \(\sin(t)>0\) and \(\cos(t)<0\), the terminal point lies in Quadrant II.
• (c) For \(\sin(t)>0\) and \(\cos(t)>0\), the terminal point lies in Quadrant I.
• (d) For \(\sin(t)<0\) and \(\cos(t)>0\), the terminal point lies in Quadrant IV.

Answer:

(a) III
(b) II
(c) I
(d) IV