76 - trigonometric identities · 2020-04-06 · when you’re solving trigonometric identity...

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