Been 20 years since I've identified trig identities. We are stuck on a particular type and would appreciate some explanation. 1/sin(-x) * (1-cos^2x) that's cos(squared x) and 1+1/cos(-x) / -sinx-tanx

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- May 19th 2008, 08:05 PMsingleton2787trigonometric identity
Been 20 years since I've identified trig identities. We are stuck on a particular type and would appreciate some explanation. 1/sin(-x) * (1-cos^2x) that's cos(squared x) and 1+1/cos(-x) / -sinx-tanx

- May 19th 2008, 08:10 PMMathstud28
- May 19th 2008, 08:23 PMsingleton2787problem re-written
Problem 1 (simplify) 1/sin(-x) * (1-cos^2x)

- May 19th 2008, 08:28 PMMathstud28
- May 19th 2008, 08:35 PMsingleton2787i dont understand..
how does ?

- May 19th 2008, 08:40 PMMathstud28
Because

This can be derived multiple ways...the most intuitive being

On the unit circle which has a radius of one any of the points on the circle have coordinates

So the distance from the origin to any point on the circle which I stated earlier is 1

So setting up the distance equation we have

Simplifying we get

Usually in trig classes this indentity is just taken to be true - May 19th 2008, 08:53 PMsingleton2787second problem
thanks for your help can you explain this one?

- May 19th 2008, 09:18 PMReckoner
First, convert everything to sines and cosines using the identities

Then, combine the fractions in the numerator and denominator, reduce, factor and cancel, and you should be left with if you do it right. When working this one, it may be helpful to observe that, since sine is an odd function and cosine is even,

If you have difficulty with the simplification, let us know.