Expand $$\sin(75^{o})$$ using sum identities.

$$\sin(75^{o}) = \sin(33^{o} + 42^{o}) = \sin 33^{o} \cos 42^{o} + \cos 33^{o} \sin 42^{o}$$ .

Expand $$\cos(\frac{\pi}{5} + \frac{\pi}{6})$$ using sum identities.

$$\cos(\frac{\pi}{5} + \frac{\pi}{6}) = \cos\frac{\pi}{5} \cos\frac{\pi}{6} - \sin\frac{\pi}{5} \sin\frac{\pi}{6}$$ .

What is the value of $$\cos(20)\cos(40) - \sin(20)\sin(40)$$ ?

The value is $$\cos(20 + 40) = \cos(60) = \frac{1}{2}$$ .

What is the value of $$\cos(75^{o})\cos(15^{o}) - \sin(75^{o})\sin(15^{o})$$ ?

The value is $$\cos(75^{o} + 15^{o}) = \cos(90^{o}) = 0$$ .

Find the exact value of $$\sin(5\pi/12)\cos(\pi/4) - \cos(5\pi/12)\sin(\pi/4)$$ .

The value is $$\sin(5\pi/12 - \pi/4) = \sin(\pi/3) = \frac{\sqrt{3}}{2}$$ .

What is the relationship between sine and cosine in the context of sum and difference identities?

Sine and cosine are related through their identities, where sine can be expressed in terms of cosine and vice versa, especially in sum and difference formulas.

What is the angle addition formula for sine?

The angle addition formula for sine is $$\sin(a + b) = \sin a \cos b + \cos a \sin b$$ .

What is the angle subtraction formula for cosine?

The angle subtraction formula for cosine is $$\cos(a - b) = \cos a \cos b + \sin a \sin b$$ .

How can you derive the sine of a sum from the unit circle?

The sine of a sum can be derived from the unit circle by considering the coordinates of points corresponding to angles a and b.

What is the significance of the angle difference identity in trigonometry?

The angle difference identity allows for the simplification of expressions involving the sine and cosine of angle differences, making calculations easier.

Provide an example of using the cosine difference identity.

Using the cosine difference identity: $$\cos(75^{o} - 15^{o}) = \cos 75^{o} \cos 15^{o} + \sin 75^{o} \sin 15^{o}$$ .

Sum and Difference Identities Flashcards

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1.

FLASHCARD QUESTION

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What is the sum identity for sine?

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2.

FLASHCARD QUESTION

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What is the difference identity for sine?

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CCSS.HSF.TF.C.9

3.

FLASHCARD QUESTION

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What is the sum identity for cosine?

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CCSS.HSF.TF.C.9

4.

FLASHCARD QUESTION

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What is the difference identity for cosine?

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CCSS.HSF.TF.C.9

5.

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CCSS.HSF.TF.C.9

6.

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CCSS.HSF.TF.C.9

7.

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CCSS.HSF.TF.C.9

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