1. Where does sinx^2+cosx^2=1 come from?
In earlier units we learned about the three basic trig functions which are sin, cosine, and tangent. Sine which means x/r so the y is the side that rises and r is the hypotenuse. R replaces the c^2 in the Pythagorean theorem. So it would really be a^2+b^2=R^2. Cosine we know is y/r . We know that when looking at the problem above that it really is x/r^2+y/r^2=1. Using the unit circle to help prove that this statement is true is fairly easy we use the 45-45-90 triangle. Which is square root of 2/2, square root of 2/2. When squaring these you get one half plus one half equals one. Which in this case is an identity which means it is a true proven statement.
2. Show and explain how to derive the two remaining Pythagorean Identities from sin^2x+cos^2x=1
To derive the two remaining identities all you have to do is divide by either cosine or sine. We know that if we divide by the same function we will get one so that is how we get the one on the right side. We will also notice that if we divide by a trig function like sin/cos we simplify that to x/r /y/r we multiply the reciprocal of the denominator to top and bottom to get the new one which is tangent. You do the same thing for the other identity.
Inquiry Reflection Activity
1. The connection I see between Units N, O, and P are that we still have to use the unit circle in some we and that we still use the trig functions even more.
2. If I had to describe trigonometry in 3 words, they would be challenging, depressing, frustrating.
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