AP Precalculus Flashcards: Sine Cosine And Tangent

What this deck covers

This deck focuses on Sine Cosine And Tangent, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Find $\text{tan}(\frac{\pi}{4})$ using the unit circle.

Answer:

1. This is a standard angle value on the unit circle.

Flashcard 2: What is the value of $\text{cos}(\text{\textpi})$?

Answer: -1. At $\pi$, the point is $(-1, 0)$ on the unit circle.

Flashcard 3: What is the cosine of $60^\text{o}$?

Answer: $\frac{1}{2}$. From the $30°-60°-90°$ triangle or unit circle.

Flashcard 4: Convert $\frac{\pi}{3}$ radians to degrees.

Answer: $60^\circ$. Use the formula $\text{degrees} = \text{radians} \times \frac{180^\circ}{\pi}$

Flashcard 5: What is the period of the tangent function?

Answer: $\pi$. Tangent repeats its values every $\pi$ radians.

Flashcard 6: What is the tangent of $45^\text{o}$?

Answer:

1. In a $45°-45°-90°$ triangle, opposite equals adjacent.

Flashcard 7: What is the general solution for $\text{sin}(x) = 0$?

Answer: $x = n\text{\textpi}$, where $n \text{ is an integer}$. Sine equals zero at integer multiples of $\pi$.

Flashcard 8: Find the cosine of angle $B$ if $\text{sin}(B) = \frac{5}{13}$ and $B$ is in Quadrant I.

Answer: $\frac{12}{13}$. Use $\sin^2 B + \cos^2 B = 1$ to find $\cos B = \sqrt{1 - (\frac{5}{13})^2}$.

Flashcard 9: Convert $45^\text{o}$ to radians.

Answer: $\frac{\text{\textpi}}{4}$. Use the formula $\text{radians} = \text{degrees} \times \frac{\pi}{180°}$.

Flashcard 10: What is the phase shift of $y = \sin(x - \frac{\pi}{4})$?

Answer: $\frac{\pi}{4}$ to the right. A negative value inside parentheses shifts the graph right.

Flashcard 11: Which quadrant has positive sine and cosine values?

Answer: Quadrant I. All trigonometric functions are positive in Quadrant I.

Flashcard 12: What is the value of $\tan(\pi)$?

Answer:

1. Since $\tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1}$.

Flashcard 13: What is the phase shift of $y = \cos(x + \frac{\pi}{6})$?

Answer: $\frac{\pi}{6}$ to the left. A positive value inside parentheses shifts the graph left.

Flashcard 14: What is the reciprocal of tangent?

Answer: Cotangent. Cotangent is $\frac{1}{\tan(x)}$.

Flashcard 15: What is the sine of $30^\text{o}$?

Answer: $\frac{1}{2}$. From the $30°-60°-90°$ triangle or unit circle.

Flashcard 16: Find $\sin\left(\frac{\pi}{6}\right)$ using the unit circle.

Answer: $\frac{1}{2}$. This is a standard angle value on the unit circle.

Flashcard 17: State the definition of tangent in a right triangle.

Answer: Tangent is the ratio of the opposite side to the adjacent side. This is the basic TOA definition from SOH-CAH-TOA.

Flashcard 18: Find $\cos\left(\frac{\pi}{3}\right)$ using the unit circle.

Answer: $\frac{1}{2}$. This is a standard angle value on the unit circle.

Flashcard 19: What is the amplitude of $y = 3\text{sin}(x)$?

Answer:

1. The coefficient of the sine function is the amplitude.

Flashcard 20: What is the general solution for $\sin(x) = 0$?

Answer: $x = n\pi$, where $n \text{ is an integer}$. Sine equals zero at integer multiples of $\pi$.

Flashcard 21: What is the tangent of $0^\text{o}$?

Answer:

1. Since $\tan(0^\circ) = \frac{\sin(0^\circ)}{\cos(0^\circ)} = \frac{0}{1}$.

Flashcard 22: What is the value of $\cos(\pi)$?

Answer: -1. At $\pi$, the point is $(-1, 0)$ on the unit circle.

Flashcard 23: State the definition of cosine in a right triangle.

Answer: Cosine is the ratio of the adjacent side to the hypotenuse. This is the basic CAH definition from SOH-CAH-TOA.

Flashcard 24: State the Pythagorean identity involving sine and cosine.

Answer: $\text{sin}^2 \theta + \text{cos}^2 \theta = 1$. This comes from the Pythagorean theorem applied to the unit circle.

Flashcard 25: What is the reciprocal of cosine?

Answer: Secant. Secant is $\frac{1}{\cos(x)}$.

Flashcard 26: Convert $\frac{\text{\textpi}}{3}$ radians to degrees.

Answer: $60^\text{o}$. Use the formula $\text{degrees} = \text{radians} \times \frac{180°}{\pi}$.

Flashcard 27: What is the tangent of an angle in Quadrant IV?

Answer: Negative. Tangent is negative in Quadrants II and IV.

Flashcard 28: What is the value of $\text{sin}(\text{\textpi})$?

Answer:

1. At $\pi$, the point is $(-1, 0)$ on the unit circle.

Flashcard 29: What is the amplitude of $y = -2\text{cos}(x)$?

Answer:

1. The absolute value of the coefficient is the amplitude.

Flashcard 30: Find $\tan(\frac{\pi}{4})$ using the unit circle.

Answer:

1. This is a standard angle value on the unit circle.

Flashcard 31: Find the tangent of angle $C$ if $\text{sin}(C) = \frac{3}{5}$ and $C$ is in Quadrant I.

Answer: $\frac{3}{4}$. First find $\cos C = \frac{4}{5}$, then $\tan C = \frac{\sin C}{\cos C}$.

Flashcard 32: What is the period of the cosine function?

Answer: $2\pi$. Cosine repeats its values every $2\pi$ radians.

Flashcard 33: What is the vertical shift of $y = \text{tan}(x) + 3$?

Answer: 3 units up. Adding a constant outside the function shifts vertically.

Flashcard 34: What is the period of the sine function?

Answer: $2\pi$. Sine repeats its values every $2\pi$ radians.

Flashcard 35: What is the value of $\text{tan}(\text{\textpi})$?

Answer:

1. Since $\tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1}$.

Flashcard 36: What is the reciprocal of sine?

Answer: Cosecant. Cosecant is $\frac{1}{\sin(x)}$.

Flashcard 37: What is the reference angle for $\frac{7\pi}{6}$?

Answer: $\frac{\pi}{6}$. Reference angle is $\frac{7\pi}{6} - \pi = \frac{\pi}{6}$.

Flashcard 38: What is the cosine of an angle in Quadrant III?

Answer: Negative. Cosine is negative in Quadrants II and III.

Flashcard 39: Find the sine of angle $A$ if $\text{cos}(A) = \frac{3}{5}$ and $A$ is in Quadrant I.

Answer: $\frac{4}{5}$. Use $\sin^2 A + \cos^2 A = 1$ to find $\sin A = \sqrt{1 - (\frac{3}{5})^2}$.

Flashcard 40: What is the cosine of $0^\text{o}$?

Answer:

1. At $0°$, the point is $(1, 0)$ on the unit circle.

Flashcard 41: What is the reference angle for $210^\text{o}$?

Answer: $30^\text{o}$. Reference angle is $210° - 180° = 30°$.

Flashcard 42: What is the sine of $90^\text{o}$?

Answer:

1. At $90°$, the point is $(0, 1)$ on the unit circle.

Flashcard 43: State the definition of sine in a right triangle.

Answer: Sine is the ratio of the opposite side to the hypotenuse. This is the basic SOH definition from SOH-CAH-TOA.