Find an angle 0 with 0 F360 = that has the same:Sine function value240degreesCosine function value as 240 degrees...

Find the reference angle and the exact function value if it exists. $$\tan 240^{\circ}$$

So in the question we have tried econometric function which is Than 220 240°. So we have to find out the reference angle and the exact function value. So Here we have, the angle is given which is 240°. So we can describe it a little bit here. So it will be 240 degree by 90 degree. two times 90° Plus two times 90° two times 90 degree. That's 60 degree. So here we can easily put the uh we can easily find out the terminal side in the quadrants. So as it is a positive value so we can grow through the Uh quadrants anti clockwise. So it will cross two quadrants as we know that one quadrants covers 90° each. So let's start from here will cost 22 quadrants here And the next coordinate across 60°. So it'll across 60 degree here, so less. I'd rather terminal side, so it's the terminal side. And we know the reference angle of any angle is the acute angle formed by the criminal side. And the X. X. Is. So from this definition we can uh say that reference angle should be this angle, this acute angle. So we can simply find out reference single as we know that this portion uh this whole person is he goes to 1,80° and uh home. And I I mean the whole angle is 240 degree and the straight angle is 1 80 degrees. So if we minus the 1 80 degree from 240 degree, we'll get the red mark angle. So that's minus from 200 40° -123°. So it will be yeah 1 80°. So it was a 60 degree. So we have the reference angle which is 60° here. And for the function value we have is them. We can say it is uh and 200 40 degree. So as it is in the third quadrant, so it will be the anti uh equals two -Y by -6. So the function value will be in positive. So we can say it would be positive, we can say tend 60°, the function value, which will be, let's finally calculate that. We'll get that. It is rude over three only. So yes, these are the answers for the question. This is the hunk reference angle and this is the functional value. So thank you.

So we need a coach terminal angle for negative 1400 our answer has to be between zero and 3 60. This is really easy. We're just gonna keep adding positive 3 60 until you get a number between zero and 3 60 we end up hitting 40 degrees, so that is our co terminal angle right.

In this problem. I'm looking for a co terminal ales of 361 degrees. We wanted to fall between zero degrees and 360 degrees. Clearly 3 61 is larger than this interval. One rotation is 360 degrees. So if I take 361 degrees minus 360 degrees, that will give me one degree, one degrees the co terminal angle for 361 degrees.

It's very straightforward. We have 451 we want are answers to be between zero and 360. Yeah. So I take 451 and i subtract 360 and there's my answer. It's right between there and its co terminal.