- #1
Mr Davis 97
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Given that ##\cos x = -0.4927##, ##\sin x = \pm \sqrt{1 - (\cos x)^2} = \pm \sqrt{1 - (-0.4927)^2} = \pm 0.8704##. How do I know which sign to choose for the correct sign?
You don't. You will need some other fact to make that choice.Mr Davis 97 said:Given that ##\cos x = -0.4927##, ##\sin x = \pm \sqrt{1 - (\cos x)^2} = \pm \sqrt{1 - (-0.4927)^2} = \pm 0.8704##. How do I know which sign to choose for the correct sign?
That's too open-ended. What other informmation do you have? Or is this a generic question?Mr Davis 97 said:Oh. Like what extra information would I need?
You need some way to determine whether x is in 2nd or 3rd quadrant, yes.Mr Davis 97 said:Just a generic question. Would I need to know what quadrant cosx is in? Since it could be in either II or III.
They BOTH are correct. You make a selection according to the situation you are solving.Mr Davis 97 said:Given that ##\cos x = -0.4927##, ##\sin x = \pm \sqrt{1 - (\cos x)^2} = \pm \sqrt{1 - (-0.4927)^2} = \pm 0.8704##. How do I know which sign to choose for the correct sign?
You would need to know what quadrant x is in, not what quadrant cos(x) is in.Mr Davis 97 said:Would I need to know what quadrant cosx is in?
The sine and cosine functions are two of the most important trigonometric functions. They are related to each other through the Pythagorean identity: sin2(x) + cos2(x) = 1. This means that for any angle x, the square of the sine of x plus the square of the cosine of x will always equal 1.
To determine the sign of sinx given cosx, you need to know the quadrant in which the angle x lies. In quadrant I, both sinx and cosx are positive. In quadrant II, sinx is positive and cosx is negative. In quadrant III, both sinx and cosx are negative. And in quadrant IV, sinx is negative and cosx is positive.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on the coordinate plane. It is used to visualize the values of the sine and cosine functions for any given angle. By looking at the coordinates of a point on the unit circle, you can determine the sign of sinx and cosx for that angle.
No, the sign of sinx and cosx cannot be the same. This is because of the relationship between the two functions and the fact that their values are always between -1 and 1. So if one is positive, the other must be negative and vice versa.
The sign of sinx and cosx will change as the angle x increases because the values of these functions oscillate between positive and negative as the angle increases. In general, as the angle increases from 0 to 90 degrees, the sign of sinx and cosx will change from positive to negative. As the angle continues to increase, the signs will continue to alternate between positive and negative.