INQUIRY ACTIVITY SUMMARY
a. An identity is a proven formula and fact that are always true. The Pythagorean Theorem is an identity because it is a proven formula that is true.
b. The Pythagorean theorem is x^2+y^2=r^2.
c. If you wanted x^2+y^2=r^2 to equal 1 you will need to divide r^2 to the other side and you are left with x^2/r^2 +y^2/r^2=1. However, we can rewrite that and say (x/r)^2+(y/r)^2=1 because of the distributive property of a power.
d. The ratio for cosine on the unit circle is x/r.
e. The ratio for sine on the unit circle is y/r.
f. We can plug in cosine for x/r in the Pythagorean theorem(x/r)^2+(y/r)^2=1 and sin for y/r. We can conclude that the Pythagorean theorem is cos^2theta+sin^2theta=1.
g. Sin^2theta+cos^2theta=1 is referred to as a Pythagorean identity because we can plug in cosine for x/r in the Pythagorean theorem (x/r)^2+(y/r)^2=1 and sin for y/r and it is still the Pythagorean theorem but in words because the trig function for cos was x/r and sin's trig function was y/r. Therefore, it is the same as (x/r)^2+(y/r)^2=1 because we know the trig function for cos was x/r and sin's trig function was y/r.
INQUIRY ACTIVITY REFLECTION
1. The connections that I see between Units N, O, P, and Q so far are the unit circle provided us with the ordered pairs of trig function and then we wan use those trig functions to solve for missing angles and sides of special right triangles and non-right triangles and now we can use the unit circle trig functions and ordered pairs to rewrite the Pythagorean theorem. Perhaps, we can use those trig functions and the Pythagorean theorem to now find missing angles and sides of special right triangles.
2.If I had to describe trigonometry in THREE words, they would be algebra geometry combined.