Inquiry activity summeryWhere does sin^2x+cos^2x=1 ?
it comes form the Pythagorean theorem. and the Pythagorean theorem is an identity its self.
What is the Pythagorean theorem using x,y and r?
the equation is A^2+B^2=C^2. when we plot the coordinate plane using the unit circle we get X^2+Y^2=R^2. x is the horizontal leg y the vertical leg and r the hypotenuse. and r being the hypotenuse make the equation equal to 1.
Pythagorean theorem equals to 1
as you can see this is just the Pythagorean theorem when you divide the R and it shows how cos and sin are in the equation. x/r being cos and y/r being sin. we when can consider it an identity.
showing that the identity is true.
drive the identity with secant and tangent
to find it we divide the equation by cos^2x
and as you simplify the equation it turn out
drive the identity with cosecant and cotangent
to find this we divided the equation by sin^2x
and like the top equation we simplify and we find it.
inquiry activity reflection
1. i have realize that in the few unites we have learned that all interconnect with each other.
2. if i had to describe trigonometry in three words i would describe them as interesting, hard, and fun.
i really like this unit and how it all connects. it makes you think and use the other chapters to think about it and.
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