(a) On the diagram, sketch the graph of $y = \cos x$ for $0^\circ \leq x \leq 360^\circ$.
(b) Solve the equation $\cos x = -\frac{1}{2}$ for $0^\circ \leq x \leq 360^\circ$.
▶️ Answer/Explanation
(a) 
The cosine graph should start at (0°,1), decrease to (180°,-1), and return to (360°,1), forming a smooth wave.
(b) $x = 120^\circ$ or $x = 240^\circ$
These are the angles in the range where cosine equals -1/2. 120° is in the second quadrant and 240° is in the third quadrant.
(a) 
Sketch the graph of $y = \cos x$ for $0° ≤ x ≤ 360°$.
(b) When $\cos x = 0.21$, find the reflex angle $x$.
▶️ Answer/Explanation
(a) 
Graph starts at (0,1), goes down to (180,-1), and returns to (360,1)
(b) $x = 282.1°$
(a) The cosine graph should show a complete wave from 0° to 360° starting at maximum.
(b) First find acute angle: $\cos^{-1}(0.21) ≈ 77.9°$
Reflex angle = 360° – 77.9° = 282.1°