The graphs below represent the curves of functions $f$ and $g$ defined by $f(x) = a \, sin \, x$ and $g(x) = - cos \, b \, x$ respectively for $x \in [0 \degree ; 180 \degree]$ - NSC Technical Mathematics - Question 5 - 2019 - Paper 2

From the graph, we can deduce that the amplitude of the sine function is given by the maximum height reached by $f$, which corresponds to $a = -2$.

Similarly, the cosine function $g(x) = - cos(b \, x)$ shows that the maximum value is also impacted by the coefficient $b$, which reads as $b = 2$.

The coordinates of point T, where the curves intersect, can be found on the graph. Thus,

$T(158.5\degree; -0.7)$ is an accepted answer.

For part 5.4.1, since we are looking for when the product $g(x) \, imes \, f(x) > 0$, we analyze the graph. This condition holds true for values in the interval:
$135\degree < x < 180\degree$

For part 5.4.2, $f(x)$ will be undefined at the points where $g(x)$ crosses zero:

$x = 45\degree \, or \, x = 135\degree$.