Aim: What are the identities of
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Aim: What are the identities of sin ( A ± B) and tan ( A ± B )? PowerPoint PPT Presentation


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Aim: What are the identities of sin ( A ± B) and tan ( A ± B )?. Do Now: Write the cofunctions of the following 1. sin 30  2. sin A  3. sin ( A + B ). sin ( A + B ) . = cos (90 – ( A + B )) . = cos (90 – A – B ) . = cos ((90 – A ) – B ) .

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Aim: What are the identities of sin ( A ± B) and tan ( A ± B )?

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Aim what are the identities of sin a b and tan a b

Aim: What are the identities of sin (A ± B) and tan (A ±B)?

Do Now: Write the cofunctions of the following

1. sin 30

2. sin A

3. sin (A + B)

sin (A + B)

= cos (90 – (A + B))

= cos (90 – A – B)

= cos ((90 – A) – B)

= cos (90 – A) cos B + sin (90 – A) sin B

= sin A cos B + cos A sin B

HW: p.499 # 8,14,16,18 p.502 # 8,10,20,22


Aim what are the identities of sin a b and tan a b

Let’s guess what sin (A – B) is equivalent to?

sin (A – B) = sin A cos B – cos A sinB

In additional to identities of the sum and difference of two angles of sine and cosine, let’s take a look at other identities.

sin (-A) = cos (90 –(-A)) = cos (90 + A) = cos 90 cos A – sin 90 sin A = 0(cos A) – 1(sin A)

= –sin A

cos (-A) = sin (90 – (-A)) = sin (90 + A) = sin 90 cos A + cos 90 sin A = 1(cos A) + 0(sin A) = cos A


Aim what are the identities of sin a b and tan a b

Example: Find the exact value of sin 105°

Example: Find the exact value of sin 65cos 25

+ cos 65 sin 25

sin(65 + 25) = sin 90° = 1


Aim what are the identities of sin a b and tan a b

If

A is a positive acute angle.

B is a positive obtuse angle. Find the value of sin (A – B)

sin (A – B) =sin A cos B – cos A sin B


Aim what are the identities of sin a b and tan a b

Use the same way, we can prove that


Aim what are the identities of sin a b and tan a b

Use (45 +120) = 165 to find the exact value of tan 165


Aim what are the identities of sin a b and tan a b

Find the exact value of tan (A + B) and tan (A – B)

A = 45 and B = 210

Find the exact value of tan 285

Find the exact value of tan 185


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