If $$\theta$$ is an angle in the first quadrant and $$\frac{2}{5} = \text{sin} \theta$$ , what is $$\text{cos} \theta$$ ?

Using the Pythagorean identity $$\text{sin}^2 \theta + \text{cos}^2 \theta = 1$$ , we find that $$\text{cos} \theta = \frac{\text{sqrt}(21)}{5}$$ .

How do you solve $$\text{cos}^2 \theta = \frac{1}{2}$$ for $$\theta$$ in the interval $$[0, 2\text{π})$$ ?

The solutions are $$\theta = \frac{\text{π}}{4}, \frac{7\text{π}}{4}, \frac{3\text{π}}{4}, \frac{5\text{π}}{4}$$ .

What is the solution to the equation $$2\text{cos}^2 x - 3\text{cos} x + 1 = 0$$ on the interval $$0 \text{ to } 2\text{π}$$ ?

The solutions are $$x = 0, \frac{\text{π}}{3}, \frac{5\text{π}}{3}, 2\text{π}$$ .

If $$\text{sin} x = \frac{1}{2}$$ , what is $$\text{sin}(2x)$$ ?

Using the double angle identity, $$\text{sin}(2x) = 2\text{sin}(x)\text{cos}(x)$$ . Since $$\text{cos}(x) = \frac{\text{sqrt}(3)}{2}$$ , we find that $$\text{sin}(2x) = \frac{\text{sqrt}(3)}{2}$$ .

What is the range of the sine and cosine functions?

The range of both the sine and cosine functions is from -1 to 1.

What is the unit circle and how does it relate to trigonometric functions?

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. The coordinates of points on the unit circle correspond to the values of sine and cosine for angles measured from the positive x-axis.

What is the value of $$\text{cos}(0)$$ and $$\text{sin}(0)$$ ?

$$\text{cos}(0) = 1$$ and $$\text{sin}(0) = 0$$ .

What is the formula for the cosine of a sum of two angles?

The formula is: $$\text{cos}(A + B) = \text{cos}(A)\text{cos}(B) - \text{sin}(A)\text{sin}(B)$$ .

What is the formula for the sine of a sum of two angles?

The formula is: $$\text{sin}(A + B) = \text{sin}(A)\text{cos}(B) + \text{cos}(A)\text{sin}(B)$$ .

What is the value of $$\text{sin}(\frac{\text{π}}{6})$$ ?

$$\text{sin}(\frac{\text{π}}{6}) = \frac{1}{2}$$ .

What is the value of $$\text{cos}(\frac{\text{π}}{3})$$ ?

$$\text{cos}(\frac{\text{π}}{3}) = \frac{1}{2}$$ .

What is the sine of an angle in terms of the cosine of its complement?

$$\text{sin}(\theta) = \text{cos}(90^\text{o} - \theta)$$ .

Pythagorean & Double Angle Identities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.8

3.

FLASHCARD QUESTION

Front

What are the double angle identities for sine and cosine?

Back

Tags

CCSS.HSF.TF.C.9

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.B.7

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.C.9

7.

FLASHCARD QUESTION

Front

What is the relationship between sine and cosine in a right triangle?

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, while the cosine is the ratio of the length of the adjacent side to the hypotenuse.

Tags

CCSS.HSG.SRT.C.6

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