Do Now
How does cos (-𝜃) compare with cos (𝜃)?
How does sin (-𝜃) compare with sin (𝜃)?
cos (-𝜃) = cos 𝜃
sin (-𝜃) = -sin 𝜃
cos 𝜃 = x, and the x-coordinates
of points A and B are equal, so cos (-𝜃) = cos 𝜃
sin 𝜃 = y, and the y-coordinate
of point A = 0.5, but the y-coordinate
of point B = -0.5, so sin (-𝜃) = -sin 𝜃
Puzzle # Title Page #
72 Frequency
73 Translations
74 Trig Functions over Time
75 Modeling with Trig Functions
76 Trigonometric Identies
Puzzle # 76
How are trigonometric identities derived?
(sin θ)(sin θ) = sin2 θ
Determine sin A and cos A
Determine sin2 A + cos2 A
Trigonometric Identity
sin2 θ + cos2 θ = 1
sin A =ac
sin2 A =a2
c2
cos A =bc
cos2 A =b2
c2
sin2 A + cos2 A
=a2
c2+
b2
c2
=a2 + b2
c2
Since it’s a right triangle, a2 + b2 = c2
=c2
c2
= 1
When you’re solving trigonometric identity problems
on the calculator, the calculator will put the exponent
after the angle rather than the sine, cosine or tangent.
sin(θ)2
cos(θ)2
tan(θ)2
sin2 θ + cos2 θ = 1
Determine the trigonometric identities for the following?
tan2 θ
cot2 θ
csc2 θ
sec2 θ
sin2 θ + cos2 θ = 1
Determine the trigonometric identities for the following?
tan2 θ =sin2 θcos2 θ
sin2 θcos2 θ
+cos2 θcos2 θ
=1
cos2 θ
tan2 θ + 1 = sec2 θ
tan2 θ = sec2 θ − 1
sec2 θ
sin2 θ + cos2 θ = 1
Determine the trigonometric identities for the following?
cot2 θ =cos2 θsin2 θ
csc2 θ
sin2 θsin2 θ
+cos2 θsin2 θ
=1
sin2 θ
1 + cot2 θ = csc2 θ
cot2 θ = csc2 θ − 1
Given the cosine of an angle = -0.8, what are the possible values for the sine of that angle?
Given the cosine of an angle = -0.8, what are the possible values for the sine of that angle?
sin2 θ + cos2 θ = 1
sin2 θ + (−0.8)2 = 1
sin2 θ + 0.64 = 1
sin2 θ = 0.36
sin2 θ = 0.36
sin θ = ± 0.6
Exit Card # 76
If , then M =sin2(32∘) + cos2(M) = 1
1) 32°
2) 58°
3) 68°
4) 72°
Exit Card # 76
If , then M =sin2(32∘) + cos2(M) = 1
1) 32°
2) 58°
3) 68°
4) 72°
Since , and 𝜃 = 32°,
M = 32°
sin2 θ + cos2 θ = 1