For each function, give the amplitude, period, vertical transl...

Question

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sin 5x

Accepted Answer

Welcome back. I am so glad you're here. We are asked to find the amplitude period, vertical translation and phase shift for the following trigonometric function. Our given trigonometric function is Y equals 3.5 sign of seven X. Our answer choices are answer choice. A amplitude equals 3.5 and period equals two pi divided by seven answer. Trace B amplitude equals 3.5 and period equals two pi answer choice. C amplitude equals 3.5 and period equals seven pi divided by two and answer choice. D amplitude equals seven and period equals two pi divided by seven. All right. So we are taking a look at this given sine function we recall from previous lessons that sine functions come in the format of Y equals C plus A sign of open bracket. B multiplied by the quantity of X minus D close parentheses, close bracket. Now, we can compare our given trigonometric function with the standard one to figure out our A's B's C's and D's. So comparing here A is what's being multiplied by our sine function and that is 3.5 in our given function. So A equals 3.5 B is what's being multiplied directly to the X inside of the function. And here what's being multiplied directly to the X is A seven. So B equals seven C is what's being added or subtracted to the function on the outside. And here nothing is being added or subtracted. So our C term is equal to zero and the D term is what's being added or subtracted directly to the X inside of the function. And here nothing is being added or subtracted directly to the X. So our D is also equal to zero. Well, that's great. But what does it all mean? Well, we recall from previous lessons that A is related to the amplitude, we know that the amplitude is found by taking the absolute value of A. And here our A is 3.5. So the absolute value of 3.5 equals 3.5. So our amplitude is 3.5. Next, our be B is related to the period for a sine function. We know that the period is found by taking two pi dividing that by B and since B is seven, that would be two pi divided by seven, that's already simplified. So our period is equal to two pi divided by seven. Now C and D, those are both zero here. But I'll remind you what that means C is related to a vertical translation. And since our C is equal to zero, it means there is no vertical translation for this particular function. And with D that's related to the phase shift because our D is equal to zero, it means there is no phase shift for this particular function. So we look at our answer choices for an amplitude of 3.5 in a period of two pi divided by seven. And that matches with answer choice a well done. We'll catch you on the next one.

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For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.
y = 2 sin 5x