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 $x \in [0 ; 180^\circ]$. $R(21,5^\circ; -0,7)$ and $T$ are the points of intersection of the curves of $f$ and $g$. Use the graphs above to answer the following questions. 5.1 Give the period of $f$. 5.2 Determine the numerical values of $a$ and $b$. 5.3 Write down the coordinates of $T$. 5.4 Determine the value(s) of $x$ for which: 5.4.1 $g(x) \cdot f(x) > 0$ for $x \in [90^\circ ; 180^\circ]$. 5.4.2 $f(x)$ will be undefined.

NSC Technical Mathematics Trigonometry: The graphs below represent the c

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 $x \in [0 ; 180^\circ]$ - NSC Technical Mathematics - Question 5 - 2019 - Paper 2

Question 5

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

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 $x \in [0 ; 180^\circ]$. ... show full transcript

Worked Solution & Example Answer: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 $x \in [0 ; 180^\circ]$ - NSC Technical Mathematics - Question 5 - 2019 - Paper 2

Step 1

Give the period of $f$

96%

114 rated

Answer

The period of the sine function $f(x) = a \sin x$ is $360^\circ$ . Therefore, the period of $f$ is 360.

Step 2

Determine the numerical values of $a$ and $b$

99%

104 rated

Answer

From the graph, it can be observed that the maximum value of $f(x)$ is 2, which suggests that $a = -2$ . Also, the maximum value of $g(x)$ is at 1, which suggests that $b = 2$ .

Step 3

Write down the coordinates of $T$

96%

101 rated

Answer

The coordinates of point $T$ can be determined from the graph as follows:
$T(158.5^\circ; -0.7)$ .

Step 4

Determine the value(s) of $x$ for which: g(x) \cdot f(x) > 0$ for $x \in [90^\circ ; 180^\circ]$

98%

120 rated

Answer

The product $g(x) \cdot f(x) > 0$ holds true when both functions are either both positive or both negative. Analyzing the graph, this occurs for:
$135^\circ < x < 180^\circ$ .
Thus, $x \in [135^\circ ; 180^\circ]$ .

Step 5

Determine the value(s) of $x$ for which: $f(x)$ will be undefined

97%

117 rated

Answer

The function $f(x)$ will be undefined specifically whenever the sine function oscillates. However, from the equation provided, we look for other points. Hence, $x = 45^\circ$ or $x = 135^\circ$ .

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 $x \in [0 ; 180^\circ]$ - NSC Technical Mathematics - Question 5 - 2019 - Paper 2

Worked Solution & Example Answer: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 $x \in [0 ; 180^\circ]$ - NSC Technical Mathematics - Question 5 - 2019 - Paper 2

Give the period of $f$

Determine the numerical values of $a$ and $b$

Write down the coordinates of $T$

Determine the value(s) of $x$ for which: g(x) \cdot f(x) > 0$ for $x \in [90^\circ ; 180^\circ]$

Determine the value(s) of $x$ for which: $f(x)$ will be undefined

Join the NSC students using SimpleStudy...