what is the domain of validity for csc 0=1/sin 0 This is a topic that many people are looking for. amritsang.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, amritsang.org would like to introduce to you tan(arccos(x)). Following along are instructions in the video below:
s see how can we change tangent of impressed cosine x. Into an algebraic expression expression and the first thing that we have to do is look at this part first cosine x represents an angle so we can begin by okay that angle theta equals to the inverse cosine and we can change this signal back and forth. Because i can now apply the regular cosine on both sides because this way i can cancel the regular cosines and the inverse cosine and im talking about cosine of x.
And we have to refer back cosine lets finish up causing a right triangle this means. We have adjacent over hypotenuse and were talking about cosell bingo. Its equal to x.
Well. In this case. We cant access that jasons died.
But we can put xs x. Over one so we know exist adjacent side one in stop abuse and we can draw a right triangle and the rectangle that we should draw us something like this and just join this kind of right triangle every single time. So it can be tough sister and i can put the angle right here is theta adjacent which do this right yeah.
According to my ankle. Choice details here so adjacent will be down here for the x and how come to us what we want so that will be the set up. We also need to figure out this side right here the opposite side.
But in the right triangle as soon as we fill your two sides. The three side can be found by the passage from zero. So we can show this a and we can do it something like a squared plus x.
Squared is equal to 1 squared. So i can move the x chrome. To the other side.
This is a squared equals to 1 minus. X. 1.
Square. Is 1 and take. The screw.
On both sides. A will be square root of 1 minus. X.
Squared. Take the positive square root for this. So.
For this side. The a is just square root of 1 minus. X.
Squared. And now look at this picture. And look how much you have to figure out tangent of this angle as angle.
If the data we sense of security tangent of the angle. We can use this triangle wedge and tangent is what in a right triangle tangent is the opposite over the adjacent so in this case. We are going to get the opposite is this square root of 1 minus.
X. Squared on the top over the adjacent is x. And this is it this is how we can change a composition of a regular trig function with the inverse trig function back to algebraic expressions.
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