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hello in this video we will be finding exact value of tangent of pi out of six anytime you see exact value its a problem that involves you to find one of the special angles which are usually 30 degrees or pi out of six 45 degrees or PI or 4 and 60 degrees or PI out of 3 or any of the angles that fall on X and Y axis if youre not that good with radians and not sure which degree measure to reference PI out of 6 can be easily changed
into degrees we was multiplying it by 180 degrees out of price will cancel and you get that pie out of 6 is equal to 30 degrees so finding the exact value of tangent of PI out of 6 is exactly the same problem as finding exact value of tangent of 30 degrees if you have the values memorized you can go ahead and say that tangent of 30 degrees is equal to radical 3 out of 3 but if youre not sure exactly its very easy to use reference table we have 0
1 2 3 4 take a square root of this whole thing divide everything by 2 sine reference goes from left to right we have 0 30 45 60 90 and cosine goes from right to left 0 30 45 60 or 90 tangent of 30 degrees is equal to sine of 30 degrees divided by cosine of 30 degrees so tangent of 30 degrees is equal to sine of 30 reference for that is on top of 1 so we get square root of 1 out of 2 or just one hand /
cosine of 30 reference for cosine is on top of three so we get square root of three out of two now we just need to simplify this we have one half change division into multiplication flip the second fraction so we get two out of radical 3q + 2 will cancel so we get tangent of 30 degrees is equal to one out of radical 3 which should be rationalized by multiplying denominator by square root of 3 and numerator by square root of 3 this will give us tangent of 30 degrees
we get one times radical 3 in numerator so we have radical 3 radical 3 times radical 3 we have two factors of square root of 3 in denominator square root and square will cancel and we get that tangent of 30 degrees is equal to square root of 3 out of 3 tangent of 30 degrees is equal to radical 3 out of 3 so does tangent of PI of 6 so tangent of PI of 6 is also equal to radical 3 out of 3 and this would be our solution thats all
exact value, tan, pi/6, trig
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