In Exercises 11–24, find all solutions of each equation.

tan x =...

Question

In Exercises 11–24, find all solutions of each equation.

tan x = 0

Accepted Answer

Hello everybody. I hope you're doing. All right. Today, today we're going to be looking at this question that states for the following trigonometric equation solve and give the answer in radiance where our equation is tangent of A equals undefined. Now, our answer choices are A, A is equal to pi divided by two plus pi N or N is an integer. And N will be an integer for all the answer choices as a choice B is A is equal to pi divided by two plus two. Pi N C is A is equal to three pi divided by two plus pi N and D is A is equal to three pi divided by two plus two. Pi N. No, we have an equation that is tangent. So let's recall what tangent is. We can recall that tangent of A is equal to sign of a divided by cosine of A. So for tangent to be undefined, we have that therefore, cosine of A must be, well, if cosine of A is in the denominator of our fraction, what number has to be in the denominator for a fraction to be undefined? Well, that number must be zero because you can't divide by zero. Now, with that information, we know that cosine of a must be zero. So let's recall from our unit circle values that cosine of pi divided by two equals zero and cosine of a three pi divided by two is also equal to zero. And now let's recall the period of tangent meaning when we look at the period of a trigo trigonometric equation, we're looking at its graph and after each period that graph will repeat, so the values will kind of repeat as it as it goes forward. So let's recall that tangent has a period of pi. So every pi in length on, on the graph, the graph of tangent would just continue to repeat, the shape will continue to repeat. So we have that therefore A is equal to pi divided by two plus pi N. And we add the pi N because as we mentioned, every pie units, the graph will repeat. So the angle will change. But the fi the answer of that angle will remain the same. So we have every pie and then we add the N as the integer because every pi N there will be multiple pi units and measurements going forward. So those values will repeat. So we have that A is equal to pi divided by 21 of our answers. And then we add the pi pi N to show that that will repeat as the graph continues. And we had our other answer was three pi divided by two. So we have that A is equal to three pi divided by two plus pi N. However, we can skip this solution because pi divided by two plus pi multiplied by one equals three pi divided by two. So we have our first solution. If we have an N of one, we reach our second solution. So we can eliminate the second solution altogether. And just focus on the first solution, which is A, is equal to pi divided by two plus pi N, which in our case is answer choice A. So we can see how important it is to be able to recall different values from our unit circle as well as understand how tangent works as an equation and know where the values match up. So I hope that was helpful. And until next time.

In Exercises 11–24, find all solutions of each equation. tan x = 0

Key Concepts

Tangent Function

Solutions of Trigonometric Equations

Unit Circle

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