Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g. 5.2 Draw sketch graphs of f and g on the same set of axes on the grid provided in the ANSWER BOOK. Clearly indicate ALL turning points, end points and intercepts with the axes.

NSC Technical Mathematics Functions and Graphs: Given the functions defined by

Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g - NSC Technical Mathematics - Question 5 - 2022 - Paper 2

Question 5

Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g. 5.2 Draw sketch graphs of f and g on ... show full transcript

Worked Solution & Example Answer:Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g - NSC Technical Mathematics - Question 5 - 2022 - Paper 2

Step 1

Write down the period of g.

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Answer

The function g(x) = cos(2x) is a cosine function with a coefficient of 2. The period of a cosine function is given by the formula:

$T = \frac{360°}{k}$

where k is the coefficient of x. In this case, k = 2, so the period of g is:

$T = \frac{360°}{2} = 180°.$

Step 2

Draw sketch graphs of f and g on the same set of axes.

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Answer

To draw the graphs for f(x) = sin x and g(x) = cos 2x:

Graph of f(x) = sin x:
- Starts at (0, 0) and rises to (90°, 1) then falls back to (180°, 0).
- The graph has turning points at (90°, 1) and intercepts with the x-axis at (0°, 0) and (180°, 0).
Graph of g(x) = cos 2x:
- Has a maximum at (0°, 1), a minimum at (90°, -1), and returns to (180°, 1).
- The graph intercepts the x-axis at (45°, 0) and (135°, 0) with turning points at these x-values.

Final Notes: Ensure that both graphs are clearly labeled, with points of intersection and turning points identified accurately on the axes.

Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g - NSC Technical Mathematics - Question 5 - 2022 - Paper 2

Worked Solution & Example Answer:Given the functions defined by f(x) = sin x and g(x) = cos 2x, where x ∈ [0°; 180°] 5.1 Write down the period of g - NSC Technical Mathematics - Question 5 - 2022 - Paper 2

Write down the period of g.

Draw sketch graphs of f and g on the same set of axes.

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