Graph the equation for values of x between 0° and 360° in multiples of 30°. y = 5 cos x

Question

Quizplus · Accepted Answer

The graph of y = 5 cos x is a cosine curve with an amplitude of 5 and a period of 360°. The value of the cosine function varies between -5 and 5.

For x = 0°, y = 5 cos 0° = 5. 
For x = 30°, y = 5 cos 30° = 5(√3)/2 ≈ 4.33. 
For x = 60°, y = 5 cos 60° = 5/2 = 2.5. 
For x = 90°, y = 5 cos 90° = 0. 
For x = 120°, y = 5 cos 120° = -5/2 = -2.5. 
For x = 150°, y = 5 cos 150° = -5(√3)/2 ≈ -4.33. 
For x = 180°, y = 5 cos 180° = -5. 
For x = 210°, y = 5 cos 210° = -5(√3)/2 ≈ -4.33. 
For x = 240°, y = 5 cos 240° = -5/2 = -2.5. 
For x = 270°, y = 5 cos 270° = 0. 
For x = 300°, y = 5 cos 300° = 5/2 = 2.5. 
For x = 330°, y = 5 cos 330° = 5(√3)/2 ≈ 4.33. 
For x = 360°, y = 5 cos 360° = 5.

The points on the graph form a cosine curve that starts at (0°, 5), reaches a maximum of (√3)/2 times the amplitude of 5 at (30°, 4.33), goes through a minimum of 0 at (90°, 0), reaches a maximum of (-√3)/2 times the amplitude of 5 at (150°, -4.33), goes through another minimum of 0 at (270°, 0), and ends at (360°, 5).

The graph of y = 5 cos x for values of x between 0° and 360° in multiples of 30° is shown in option C.

Graph the Equation for Values of X Between 0° and 360°