Thinking/Inquiry /15 Read the following questions and answer...

Thinking/Inquiry /15 Read the following questions and answer them in the space provided. Show your mathematical calculations. Use full sentences in your answer. See how much each question is worth. 1. Is the following graph a periodic function? Explain why or why not. [3] yes 2. Determine all the values where $\sin x = \sqrt{3} \cos x$ for $0^\circ \le x \le 360^\circ$. [4] 3. Sketch a sinusoidal graph with amplitude 5, period 16, and equation of axis $y = 1$. Sketch at least 1 cycle. [4] 4. Meg has to graph the function $y = -\sin x - 2$. Can she apply the two transformations in any order that she wants to? Explain. [4]

Transcript

00:01 Hello, in this video, we will be solving the questions of a screen where in part one, we have to find out the range, amplitude, and period of the equation y equals minus 4, cos.

00:17 Inside cost, you have 3x and we have plus 2.

00:24 First of all, let's look at the amplitude.

00:29 Now the amplitude for any equation, let's say a cost bx plus c, your amplitude is always the absolute value of a.

00:46 And therefore, in this example, our amplitude, i'm going to be am for short, is going to be four.

00:53 Very simply.

00:56 Then for period, secondly, our period is always 180.

01:06 Or if you're talking in radiance or pi over b and so our period therefore will be 180 over 3 because we have 3x inside costs and so our period here will be equal to 60 60 degrees or simply pi over 3 if you're talking in radiance so this will be our period and finally for our range the range of any cost whatsoever is from minus 1 to 1.

01:48 However, in this case, we have, first of all, a coefficient of negative 4.

01:57 So our range automatically becomes from minus 4 to 4.

02:03 However, we then also have a plus 2.

02:06 And so our range becomes minus 4 plus 2, which happens to be minus 2, and 4 plus 2, which happens to be 6.

02:12 And so our final range will simply be equal to y between, which happens to, and 4 ,000, between minus 2 and 6.

02:26 And so this is how you do the first part by simply stating the range amplitude and period of y equals negative 4 cost 3x plus 2.

02:36 In part 2, in question 2, we have to draw a couple of cycles for y equals minus 3 sine 2x plus 1.

02:46 So here again, we have y equals minus 3 sine 2x plus 1.

02:58 So let's first fall notice this plus 1.

03:00 This plus 1 will provide us with a false axis.

03:03 And this false axis is going to lie somewhere around here.

03:08 Now i'm going to make a very rough diagram.

03:11 It will not be exactly the way it's supposed to look, but it will be more than enough.

03:16 As for any sign graph, for any value of sine x, our graph goes from minus 1 to 1.

03:27 However, again, with the coefficient of negative 3, our value here would be when multiplied by 3 or minus 3, it will grow from minus 3 to simply 3.

03:45 And now finally, we have a plus 1.

03:52 1 will give us a range of minus 2 and 4, adding one on both sides...

Question

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