Transcript CC3: Prove and Apply Trigonometry Identities

CC3: Prove and Apply
Trigonometry Identities
LT: 1F I can prove the Pythagorean
identity sin2θ+cos2θ=1 and use it to
find sinθ, cosθ, or tanθ given sinθ,
cosθ, or tanθ and the quadrant.
I.) Prove and Apply
Trigonometric Identities
A.) The Pythagorean trigonometric identity is a
trigonometric identity expressing the
Pythagorean theorem in terms of trig.
Functions. Along with the sum-of-angles
formulae, it is one of the basic relations
between the sine and cosine functions, from
which all others may be derived.
A. Definition
Pythagorean Trigonometric Identity
Notice
the
plus/min
us
sin2(x)
cos2(x)=
+
1
Sum and Difference
Formulas
Notice
the order
sin(A±B)=sin(A)cos(B)±cos(A)sin(B)
cos(A±B)=cos(A)cos(B) sin(A)sin(B)
B. Visual
Using what we know about the
Pythagorean Theorem we can write
x2 + y2 = 12
To show the relation ship between
the side lengths of the right triangle
2
x
+
2
y
=1
Using what we know about the Unit
Circle we can replace x and y with .
cos2x + sin2x = 1
Goal Problems (LT 1E)
Recall & Reproductions
Suppose that
cosθ=2/5 and that
θ is in the 4th
quadrant. Find
sinθ and tanθ
exactly.
Routine
Given x is in Quadrant I, find
the value of x that makes this
statement true.
Goal Problems Answers (LT 1E)
Recall & Reproductions
Is Sine neg.
or pos. in
Q4?
Routine
Active Sense-Making
Recall & Reproductions
Routine
Round Robin around
the room
Sideways Sheet
Down at desk
Based on your Goal Problems make your plan of attack for today’s practice