What is the value of $$\sin(30^\circ)$$ ?

$$\sin(30^\circ) = \frac{1}{2}$$ .

What is the value of $$\cos(60^\circ)$$ ?

$$\cos(60^\circ) = \frac{1}{2}$$ .

Use the Sum Formula to find $$\sin(75^\circ)$$ .

$$\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ) = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$$ .

Use the Difference Formula to find $$\cos(15^\circ)$$ .

$$\cos(15^\circ) = \cos(45^\circ - 30^\circ) = \cos(45^\circ)\cos(30^\circ) + \sin(45^\circ)\sin(30^\circ) = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$$ .

Find the exact value of $$\cos(105^\circ)$$ using the Difference Formula.

$$\cos(105^\circ) = \cos(90^\circ + 15^\circ) = -\sin(15^\circ) = -\left(\frac{\sqrt{6} - \sqrt{2}}{4}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$$ .

Find the exact value of $$\sin(\frac{7\pi}{12})$$ using the Sum Formula.

$$\sin(\frac{7\pi}{12}) = \sin(\frac{3\pi}{4} + \frac{\pi}{3}) = \sin(\frac{3\pi}{4})\cos(\frac{\pi}{3}) + \cos(\frac{3\pi}{4})\sin(\frac{\pi}{3}) = \frac{\sqrt{2}}{2} \cdot \frac{1}{2} + -\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$$ .

Use the Sum Formula to find $$\sin(-15^\circ)$$ .

$$\sin(-15^\circ) = -\sin(15^\circ) = -\left(\frac{\sqrt{6} - \sqrt{2}}{4}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$$ .

Write the expression $$\cos(175^\circ)\cos(55^\circ) + \sin(175^\circ)\sin(55^\circ)$$ as a single trigonometric function.

$$\cos(175^\circ - 55^\circ) = \cos(120^\circ)$$ .

Sum/Difference Formulas Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

Define the Sum Formula for Cosine.

Back

The Sum Formula for Cosine states that for any angles A and B, @@ \cos(A + B) = \cos A \cos B - \sin A \sin B@@.

Tags

CCSS.HSF.TF.C.9

2.

FLASHCARD QUESTION

Front

Define the Difference Formula for Cosine.

Back

The Difference Formula for Cosine states that for any angles A and B, @@ \cos(A - B) = \cos A \cos B + \sin A \sin B@@.

Tags

CCSS.HSF.TF.C.9

3.

FLASHCARD QUESTION

Front

Define the Sum Formula for Sine.

Back

The Sum Formula for Sine states that for any angles A and B, @@ \sin(A + B) = \sin A \cos B + \cos A \sin B@@.

Tags

CCSS.HSF.TF.C.9

4.

FLASHCARD QUESTION

Front

Define the Difference Formula for Sine.

Back

The Difference Formula for Sine states that for any angles A and B, @@ \sin(A - B) = \sin A \cos B - \cos A \sin B@@.

Tags

CCSS.HSF.TF.C.9

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

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