Aim What are the identities of sin A

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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) = 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, 22

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

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

Example: Find the exact value of sin 105° Example: Find the exact value of

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

If A is a positive acute angle. B is a positive obtuse angle. Find

If A is a positive acute angle. B is a positive obtuse angle. Find the value of sin (A – B) = sin A cos B – cos A sin B

Use the same way, we can prove that

Use the same way, we can prove that

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

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

Find the exact value of tan (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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Aim What are the identities of sin AAim What are the identities of sin A