NAME: __________________________________________________
DATE: ___________________
Algebra 2: Lesson 13-7 Proving Pythagorean Identities
Learning Goals:
1. What is a Pythagorean Identity?
2. How can we use the Pythagorean Identity to find the values of the sine, cosine, and tangent of
an angle?
IDENTITIES
In mathematics, an IDENTITY is an equation that is
. Identities are very
useful and can help us make “replacements” that may be useful when simplifying trigonometric
expressions.
RECALL THE RIGHT TRIANGLE WE MADE FROM THE UNIT CIRCLE:
Using this, we can prove the Pythagorean Identity:
What happens if you take the Pythagorean Identity
and divide each term by
?
What happens if you take the Pythagorean Identity
and divide each term by
?
Sign Chart (ASTC):
Sin θ is positive (QII)
All functions are positive (QI)
Tan θ is positive (QIII)
Cos θ is positive (QIV)
Pythagorean Identity:
Use the Pythagorean Identity to answer the following questions.
Problem
1) An angle, has a terminal ray that falls in the second
quadrant. If it is known that
determine the value
of
2) An angle, has a terminal ray that falls in the first
quadrant and
Determine the value of
in
simplest radical form.
My notes/Important Information
3) Suppose
and
the value of
4) If
√
. What is
?
√
, what are possible values of
?
5) If
and
, find cosΘ
6) If the terminal ray of
lies in the fourth
√
quadrant and
determine
and
in simplest form.
7) Use the Pythagorean identity
, where is any real number, to find
the following:
, given
.
for
Problem:
8) If the terminal side of angle , in standard position, passes
through point
, what are the numerical values of the six
trig functions?
9) If the terminal side of angle , in standard position, passes
through point
, what are the numerical values of the
six trig functions?
My notes: