Download θ sin(90°– θ)

TRIGONOMETRY
y
 1 3
 ,

2 2 
600
450
30 0
TRIG IDENTITIES2 NAME____________________
 2 2
,


 2 2 
COFUNCTION
RELATIONSHIPS
y
P’ (b,a)
90 0 – θ
 3 1
, 

 2 2
P (a,b)
θ
θ
x
Note in the unit circle diagram the
pattern that repeats itself.
x
Note the two congruent triangles whose
vertices P and P’ are shown.
Witness how the coordinates are switched.
4. a) Complete the following table:
θ 90°– θ
cscθ sin(90°– θ) secθ cos(90°– θ) cotθ tan(90°– θ)
0
30
45
60
90
b) Fill out the identities below from your conclusions using the table above.
cos(90° – θ) = _________ csc(90° – θ) = _________ cot(90° – θ) = _________
sin(90° – θ) = _________ sec(90° –θ) = _________ tan(90° – θ) = _________
5. PYTHAGOREAN IDENTITIES:
cos2θ + sin2θ = 1
Recall that applying the Pythagorean theorem on any angle θ in the unit circle gives us:
a) Hence, sin2θ = 1 – cos2θ or
cos2θ = __________.
b) Divide every term on both sides of the boxed equation by cos2θ.
sec2θ = ___________
c) Divide every term on both sides of the boxed equation by sin2θ.
csc2θ = ___________