Question 662885
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No, I can't explain it to you like you were 5.  If you need it explained like you are 5, come back and ask the question again in 10 years so I can explain it to you like you were 15.


Look at the unit circle.  The *[tex \LARGE sin] of the angle between the terminal ray and the positive *[tex \LARGE x]-axis is the *[tex \LARGE y]-coordinate of the point of intersection between the terminal ray and the unit circle.  Likewise, the *[tex \LARGE cos] is the *[tex \LARGE x] coordinate of that point.  *[tex \LARGE y]-values are positive in the I and II quadrants, negative in the III and IV quadrants. *[tex \LARGE x]-values are positive in I and IV quadrants and negative in II and III quadrants.  Since the tangent function is the quotient of sine over cosine, the tangent function is positive in the quadrants where sine and cosine have the same sign, i.e. I and III and negative where they are opposite, II and IV.


Determining which quadrant the angle 1.7 lies is dependant on whether you are measuring the angle in degrees or in radians.  I highly suspect radians, but don't like to make assumptions and since you didn't specify...


If it means degrees, then clearly it is less than 90 degrees and therefore clearly in the first quadrant.  However, if it is radians, then you have to decide whether 1.7 lies in the interval *[tex \LARGE \frac{\pi}{2}\ \leq\ \theta\ \leq \pi], that is Quadrant II, or in the interval *[tex \LARGE 0\ \leq\ \theta\ \leq\ \frac{\pi}{2}], that is Quadrant I.


<img src="http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png">


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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