In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst. 6.1 Skets die grafiek van $g(x)=2 ext{sin}x-1$ vir die interval $x ext{ } [-270^ ext{°}; 90^ ext{°}]$ op die rooster wat in jou ANTWOORDEBOOK verskaf word. Toon AL die afsnitte met die assa, asook die draaipunte. 6.2 Gestel $A$ is 'n snypunt van die grafieke van $f$ en $g$. Toon dat die $x$-koördinaat van $A$ die vergelyking $ ext{sin} x = -rac{1+ ext{√}5}{2}$ bevredig. 6.3 Bereken vervolgens die koördinates van die snypunte van grafieke van $f$ en $g$ vir die interval $x ext{ } [-270^ ext{°}; 90^ ext{°}]$.

Photo AI

In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst - NSC Mathematics - Question 6 - 2017 - Paper 2

Question 6

$In-die-diagram-is-die-grafiek-van-$f(x)=-ext{cos}2x$-vir-die-interval-$x--ext{-}--ext{-}-[-270^-ext{°};-90^-ext{°}]$-gesketst-NSC Mathematics-Question 6-2017-Paper 2.png$

In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst. 6.1 Skets die grafiek van $g(x)=2 ext... show full transcript

Worked Solution & Example Answer:In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst - NSC Mathematics - Question 6 - 2017 - Paper 2

Step 1

Skets die grafiek van $g(x)=2 ext{sin}x-1$

96%

114 rated

Answer

To sketch the graph of the function $g(x) = 2 ext{sin}x - 1$ , we start by determining the key features of the sine function. The amplitude of this sine function is 2, meaning it oscillates between -1 and 1.

Identify the Amplitude and Vertical Shift: The function oscillates between $1$ and $-3$ . The normal sine function $y = ext{sin}x$ has values from -1 to 1, and with the transformation for $g(x)$ , we shift this down by 1 to get $[-1, -3]$ .
Determine Intercepts and Shape: The intercept occurs at $x=0$ , with $g(0) = -1$ .
Plot Key Points: Find the points including the maximum at $(-90°, -3)$ and similar steps can be taken for other key values such as $-210°$ and $30°$ .
Draw the Graph: Connect the points smoothly to create a sinusoidal wave reflecting these transformations.

Step 2

Gestel $A$ is 'n snypunt van die grafieke van $f$ en $g$. Toon dat die $x$-koördinaat van $A$ die vergelyking $ ext{sin} x = -rac{1+ ext{√}5}{2}$ bevredig.

99%

104 rated

Answer

To find the x-coordinate of point $A$ , we start from the equation derived from equalizing $f(x)$ and $g(x)$ :

$ext{cos}2x = 2 ext{sin}x - 1$ This can be rewritten in standard quadratic form: $1 - 2 ext{sin}^2x - 2 ext{sin}x = 0$ Using the quadratic formula: $ext{sin}x = rac{-b ext{±} ext{√}(b^2 - 4ac)}{2a}$ We substitute for $a=2, b=2, c=-1$ and we find: $ext{sin}x = - rac{1+ ext{\sqrt}5}{2}$ .

Step 3

Bereken vervolgens die koördinates van die snypunte van grafieke van $f$ en $g$ vir die interval $x ext{ } [-270^ ext{°}; 90^ ext{°}]$.

96%

101 rated

Answer

To find the coordinates of the intersection points of $f$ and $g$ where $x$ is in the range $[-270°; 90°]$ :

Calculate the values: By solving $ext{sin} x = - rac{1+ ext{\sqrt}5}{2}$ , we find two specific angles based on the sine values.
Identify Reference Angles: Calculate the reference angles to find $ext{sin}^{-1}ig(- rac{1+ ext{√}5}{2}ig)$ yielding approximate values.
List Coordinates: The coordinates obtained are $(38,17°; 0,24)$ and $(-218,17°; 0,24)$ based on periodicity.

Thus, we conclude our results with the points of intersection.

In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst - NSC Mathematics - Question 6 - 2017 - Paper 2

Worked Solution & Example Answer:In die diagram is die grafiek van $f(x)= ext{cos}2x$ vir die interval $x ext{ } ext{ } [-270^ ext{°}; 90^ ext{°}]$ gesketst - NSC Mathematics - Question 6 - 2017 - Paper 2

Skets die grafiek van $g(x)=2 ext{sin}x-1$

Gestel $A$ is 'n snypunt van die grafieke van $f$ en $g$. Toon dat die $x$-koördinaat van $A$ die vergelyking $ ext{sin} x = - rac{1+ ext{√}5}{2}$ bevredig.

Bereken vervolgens die koördinates van die snypunte van grafieke van $f$ en $g$ vir die interval $x ext{ } [-270^ ext{°}; 90^ ext{°}]$.

Join the NSC students using SimpleStudy...

Gestel $A$ is 'n snypunt van die grafieke van $f$ en $g$. Toon dat die $x$-koördinaat van $A$ die vergelyking $ ext{sin} x = -rac{1+ ext{√}5}{2}$ bevredig.