A rotating beacon is located at point A, 4 m from a wall. The ...

Question

A rotating beacon is located at point A, 4 m from a wall. The distance a is given by

a = 4 |sec 2πt|,

where t is time in seconds since the beacon started rotating. Find the value of a for each time t. Round to the nearest tenth if applicable.

t = 1.24

Accepted Answer

Welcome back. I am so glad you're here. We're told that a rotating light is placed at the top of a pole with a height of 7 m. Use the equation D equals seven, multiplied by the absolute value of the C can of two pi T to find the distance D when T equals 2.46 seconds, then we're given a graph. We've got this figure of a triangle and you can see from point A on the ground up going straight up, we have our light, our rotating light and then D is the distance from the light to another point on the ground, which is point B and D is the hypotenuse of a triangle. And presumably this is a right triangle and angle A is going to be our right angle. The distance from a, the ground straight up the light pole to the light is labeled 7 m. Our answer choices are answer choice. A 8.7 m. Answer choice B 34.0 m. Answer choice C 7.2 m and answer choice D 3.5 m. All right. So we've only got two variables in this given equation D and TD is what we're solving for and T is given to us so we can go ahead and plug T in. So we know that D equals seven multiplied by the absolute value of the C can't of two pi and then instead of T that two pi is multiplied by 2.46. And so now it's just a matter of putting this into the calculator. Now, most calculators do not have AC C A button. If yours doesn't, then we recall from previous lessons that C can is a reciprocal function of cosign. So we know that the C can of an angle, we'll say theta is equal to one divided by the cosine of the angle theta. So here we can bring this down, we'll have seven multiplied by the absolute value of. Now, instead of using C camp, we'll have one divided by the cosine of. And then our angle is still that two pi multiplied by 2.46. So now you can plug this into the calculator. If you plug in one divided by the cosine of two pi multiplied by 2.46 you'll get a negative 1.0324 that's still in absolute value bars and still multiplied by seven. Well, the absolute value of negative 1.0324 and I rounded that, that would keep going would be a positive 1.0324. That's being multiplied by the seven. And when you multiply that by seven, you'll get about 7.22. And since all of our answer choices, our are given one decimal place. We can round this 27.2 and then don't forget we're in meters. So we look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

A rotating beacon is located at point A, 4 m from a wall. The distance a is given by
a = 4 |sec 2πt|,
where t is time in seconds since the beacon started rotating. Find the value of a for each time t. Round to the nearest tenth if applicable.
<IMAGE>
t = 1.24

Key Concepts

Secant Function

Trigonometric Functions and Time

Rounding and Precision

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