1. The equation sin2x+cos2x=1 is derived from the Pythagorean Theorem. The Pythagorean Theorem, as we know, is x^2+ y^2= r^2 when it is compared to the unit circle. To derive the equation given, we must follow the steps given on the picture below. We must first divide by r^2. This will allow us to get certain trig functions. These trig functions will be able to be arranged so that we end up having cos^2 + sin^2=1.
2. To derive the next two pythagorean identities, we must use the first pythagorean identity to get the next two. For the first one, we must divide everything by sin^2. This will create new trig ratios which will soon be simplified to make the new equation cot^2+ 1= csc^2.
To get the next pythagorean identity, we have to start off using the first pythagorean identity that we derived. From here, we must divide the entire equation by cos^2. This will again make new trig functions that will be able to simplified into the new equation, 1+ tan^2= sec^2.
Inquiry Activity Reflection
1. The connections that I see between units N,O,P,& Q so far are that they all basically rely on the Pythagorean Theorem in some way. They all also fall under the concept of the unit circle and the "magic three" ordered pairs.
2. If I had to describe trigonometry in three words, they would be tricky, mind-blowing, and interesting.
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