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2, y =sin x > cos % 0 <<4#/* abouty = -1by eci-J = 0, > ~cos'g, ~m/2 <* < #/2 (a) About the x-axis (6) About y...

Question

2, y =sin x > cos % 0 <<4#/* abouty = -1by eci-J = 0, > ~cos'g, ~m/2 <* < #/2 (a) About the x-axis (6) About y

2, y =sin x > cos % 0 <<4#/* abouty = -1 by eci- J = 0, > ~cos'g, ~m/2 <* < #/2 (a) About the x-axis (6) About y



Answers

Sketch the graph over $[0,2 \pi] .$
$$ f(\theta)=\cos \left(2\left(\theta-\frac{\pi}{2}\right)\right) $$

Okay when I'm graphing trig functions like this I start with my basic coastline function that I have memorized. It's why values at the key X values go 10 negative 101 In this case my angle is different. So what I do is I say if this angle Takes on all the values from 0 to 2 pi then I'll have one cycle of co sign following this pattern. So two theta minus pi over two. Between zero and 2 pi means that tooth data. We'll go from zeroed from Pirates 2 to 5 pirate too. And theta will take on the values from pi over four 25 Pi over four. So I draw an X. Axis Pi over four pi over two pie. three pi over 2 2 pi do do do two 123 However two Pi 3 pi over 2 2 pi. That's in the wrong place sorry. And then 1234 pipes. So what I've chosen This interval tells me from pi over four 25 pi over four, I'm going to draw 1123 45. This is five or 4, This is 55 or four. The difference between these is pie, that's the period of the graph. The period is given by two Pi divided by the coefficient of data. So the interval where I'm going to graph a cosign function is from pi 25 power four. The next one is going to be from pi over four 1234 up to nine pi over four, 95 or 41234 Up to 13 pi over four. And I'm gonna draw coastline curves. 10 -1010 -10 10 -101 needs to be more concave the other way. Now if I keep going backwards I'll pass through the origin, some teachers will ask you to rename it just by the way. Do you see that from here to here, which is pi that I have a sign curve. My period is only pie, but I do have a sign curve. So this could be written by the way, as white will sign of two. Theta start while you're graphing things, looking for other names. Other ways to name the curve. Anyway, there's your graph. Thanks for listening. Have a great day.

We have. Why is equal to cause to Tita Now, if you see we know that course off Pita is equal toe cause off by plus teeter and businesses to for every Digna Matic function. Now, if you see we feel replaced state of it to Tita because we have a duty Dahlia, we have cause to teeter is equals to cause off by plus teeter No, If you dig two comments or discourse off twice off by bless Thida and if you see carefully, let's move the stool. So it's cost. It does it will look by Nurse Tita. Okay, Like this too is an additional ones with little eyes. Tita and Pi plus data between is that the period off this function period is fight bucket A period off. The cost to treat a function list by Mr Graf would be repeating every time Act by selects mug zero. Well, knocking by remarking to buy okay on what will be the maximum the minimum value It would be seen that is minus one and plus one letter mark a line off last one. Similarly, let's marker line off minus one now at by it should be one are this. It should be one to bite. Should be one act by. By do it should be minus one at three. Pie by do it should be minus one. So it is minus one at these two points. So let's draw graphs like this, so we'll be doing a graph. So let's draw this point. Similarly, this will be the graph, so you can see this is the graph of course to Tita.

The half of the number 1 95 in which one has given us sign. Universe. Cossacks. Less cause universe syntax. Let's cause inverse. Synnex. We need to find everybody. X. So uh you know that sign universe. Ex placed course. Universe sex equal to pivot to this huddle. This hardly matters here because you'll be just being like fine words, concepts that Scotland will sign it. So let us right to them. Uh the farmer sign. So this is sign. Universe signed by by two minus theta. And private to Minnesota is always caused theater. Let's cause inverse. Cause bye bye to minus theta. So this is by the way to minus theta. Plus by by two minus theta By -2. Theatre. Now let us or differentiate. So this becomes equal to the web. I This is X. Not data X. There's a complimentary angle formula D whereby the X will be equal to. I'm sorry for this. There's there's there's Differential of the 0 -2. So -2 should be the correct answer and option number A is the correct option. Thank you.

The half of the number 1 95 in which one has given us sign. Universe. Cossacks. Less cause universe syntax. Let's cause inverse. Synnex. We need to find everybody. X. So uh you know that sign universe. Ex placed course. Universe sex equal to pivot to this huddle. This hardly matters here because you'll be just being like fine words, concepts that Scotland will sign it. So let us right to them. Uh the farmer sign. So this is sign. Universe signed by by two minus theta. And private to Minnesota is always caused theater. Let's cause inverse. Cause bye bye to minus theta. So this is by the way to minus theta. Plus by by two minus theta by minus two. Theater. Now let us or differentiate. So this becomes equal to the web. I This is X. Not data X. There's a complimentary angle formula D whereby the X will be equal to. I'm sorry for this. There's there's there's differentiation of the zero minus two. So minus two should be the correct answer and option number A is the correct option. Thank you.


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