Precal Blog

Today in class we learned about Reciprocal Trig. Functions and how they are related to their Reciprocals. To start out, our original functions are Sin of Theta = V/R, Cos of Theta = U/R, and Tan of theta = V/U. Sin’s reciprocal is CSC theta = 1/sin of Theta = R/V. Cos’s reciprocal is SEC theta = 1/Cos theta = R/U. Last, Tan’s reciprocal is COT theta = 1/Tan theta = U/R. It is very important that everyone is clear that the Reciprocals and Inverse are two DIFFERENT things. Also, remember that 1/csc = Sin theta, 1/sec = Sin theta, and 1/cot = Tan theta.

Next we moved onto an angle that contains the point (-4,-6). Sin theta = -6/sq root of 52 and csc = sq. root of 52/-6. Cos theta = -4/sq. root of 52 and sec =  sq. root of 52/-4. Tan theta = -6/-4 =3/2 and cot = 2/3 (tan is positive in the 3rd quadrant).

Lastly we found the value for all 6 trig. functions for theta = 330 degrees. Sin(30) = -1/2 and csc = 2/-1. Cos(30) = sq. root of 3/ 2 and sec = 2/sq. root of 3 (cos is positive in the 4th quadrant). Tan(30) = -1/sq. root of 3 and cot = sq. root of 3/-1.

As a side note know that, in the first quadrant all trig functions are positive, the second quadrant has only sin positive, the third quadrant has only tan positive, and in the forth quadrant only cos is positive.

PS, the next scibe is Dushan