Given: f(x) = tan x and g(x) = cos(x - 45°) for x ∈ [0°; 360°] 5.1 Draw sketch graphs of f and g on the same set of axes on the grid provided in the ANSWER BOOK - NSC Technical Mathematics - Question 5 - 2021 - Paper 2

To sketch the graphs of the functions, we first identify their key features:

Function f(x) = tan x

• Domain: f(x) is undefined at x = 90° + k*180°, where k is any integer.
• Asymptotes: Vertical asymptotes occur at x = 90° and x = 270°.
• Intercepts: The graph intersects the x-axis at multiples of 180° (0°, 180°, etc.).
• Turning Points: The maximum value occurs at 45° and minimum at 225°.

Function g(x) = cos(x - 45°)

• Domain: g is defined for all x in [0°, 360°].
• Intercepts: g(0°) = cos(-45°) = √2/2, g(90°) = cos(45°) = √2/2, g(180°) = cos(135°) = -√2/2, g(270°) = cos(225°) = -√2/2, g(360°) = cos(315°) = √2/2.
• Turning Points: The maximum and minimum values occur at x = 45° (max) and x = 225° (min).
• End Points: At x = 0° and x = 360°, the graph returns to 1.

These characteristics are used to accurately draw the graphs of f and g on the same axes, indicating key features such as intercepts and asymptotes.

Graph Illustration

While I cannot illustrate, be sure to draw the tan function with its vertical asymptotes at 90° and 270°, while the cosine function oscillates between 1 and -1 across the x-axis, intersecting at the identified points.