M 408N –Calculus for Scientists

M 408N –Calculus for Scientists - M 408N...

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M 408N –Calculus for Scientists Dr. Olena Bormashenko Notes 8/29 We will use radians instead of degrees 2 pi rad = 360 deg pi rad = 180 deg angle (a) = 180/pi * theta theta = a * pi /180 theta = 60 * pi /180 = pi/3 rad theta = 90 * pi/180 = pi/2 rad Degrees for 2pi/3 radians: a=180/pi * theta = 180/pi = 2pi/3 = [pi cancel so (180 * 2)/3 = 120] = 120 degrees Visualizing trig functions: Draw a line theta radians away from the position x axis (standard position) cos theta = x coordinate sin theta = y coordinate < theta = (cos theta, sin theta) Use the unit circle (google image) to determine cos pi/2, cos pi, and sin 0 cos pi/2 = 0 ; (x coordinate of 90 degree angle) cos pi = -1 (x coordinate of 180 degree angle) sin 0 = 0 ( y coordinate of 0 degree angle) tan theta = sin theta / cos theta (y/x) cot theta = cos theta / sin theta (x/y) csc theta = 1/sin theta (1/y) sec theta=1/cos theta (1/x) For theta between 0 and pi/2 we have the following expressions sin theta = opposite/hypotenuse ; opposite from the angle**
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M 408N &amp;acirc;€“Calculus for Scientists - M 408N...

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