Notes - Pythagorean Identity

2 ­ Notes ­ Pythagorean Identity.notebook
May 13, 2015
Pythagorean Identity
EQ: How do I use the Pythagorean Theorem to solve angles of triangles?
MCC9­12.F.TF.8 Prove the Pythagorean Identity (sin A)2 + (cos A)2 = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.
May 13­7:43 AM
The Pythagorean Identity
(sin A)2 + (cos A)2 = 1
or
sin2A + cos2A = 1
May 13­7:45 AM
1
2 ­ Notes ­ Pythagorean Identity.notebook
May 13, 2015
Proof
May 13­7:46 AM
Limits on domains
sine and cosine: [­1, 1]
tangent: (­∞,∞)
May 13­7:55 AM
2
2 ­ Notes ­ Pythagorean Identity.notebook
May 13, 2015
We find the signs of the trig functions dependent on their quadrants
Quadrant
Measure
Trig Ratios
I II III
IV May 13­7:55 AM
If sin A = 2/3 and 0o < A < 90o Find cos A
Find tan A
May 13­7:47 AM
3
2 ­ Notes ­ Pythagorean Identity.notebook
May 13, 2015
If cos A = ­3/4 and 180o < A < 270o Find sin A
Find tan A
May 13­7:47 AM
If tan A = 4/3 and 180o < A < 270o Find sin A
Find cos A
May 13­7:47 AM
4
2 ­ Notes ­ Pythagorean Identity.notebook
May 13, 2015
If sin A = ­1/3 and 3π/2 < A < 2π Find cos A
Find tan A
May 13­7:47 AM
May 13­7:57 AM
5