SAT Math Flashcards: Trigonometry

What this deck covers

This deck focuses on Trigonometry, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

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 $\text{cos}(60^\text{o})$ using cofunction identity.

Answer: $\text{sin}(30^\text{o}) = \frac{1}{2}$. Using $\cos(90° - 30°) = \sin 30°$.

Flashcard 2: Find the value of $\text{tan}^2 45^\text{o}$.

Answer:

1. Square of $\tan 45° = 1$ is 1.

Flashcard 3: Identify the reciprocal of tangent.

Answer: Cotangent (cot). Cotangent is defined as $\frac{1}{\tan}$.

Flashcard 4: Identify the cofunction identity for sine.

Answer: $\text{sin}(90^\text{o} - \theta) = \text{cos}(\theta)$. Complementary angle relationship for sine.

Flashcard 5: What is the sine of $45^\text{o}$?

Answer: $\frac{\text{sqrt}(2)}{2}$. Standard value for 45° in the unit circle.

Flashcard 6: What is the sine of $60^{\text{o}}$?

Answer: $\frac{\sqrt{3}}{2}$. Standard value for 60° in the unit circle.

Flashcard 7: State the double angle formula for tangent.

Answer: $\text{tan}(2\theta) = \frac{2\text{tan}(\theta)}{1-\text{tan}^2(\theta)}$. Formula for tangent of double angle.

Flashcard 8: What is the cosine of $60^\text{o}$?

Answer: $\frac{1}{2}$. Standard value for 60° in the unit circle.

Flashcard 9: What is the value of $\text{cos} 0^\text{°}$?

Answer:

1. At 0°, the point on the unit circle is (1,0), so cosine equals 1.

Flashcard 10: State the angle addition formula for tangent.

Answer: $\text{tan}(A + B) = \frac{\text{tan}A + \text{tan}B}{1 - \text{tan}A \text{tan}B}$. Formula for tangent of sum of two angles.

Flashcard 11: Identify the reciprocal of sine.

Answer: Cosecant (csc). Cosecant is defined as $\frac{1}{\sin}$.

Flashcard 12: What is the sine of $30^\text{o}$?

Answer: $\frac{1}{2}$. Standard value for 30° in the unit circle.

Flashcard 13: What is the range of the sine function?

Answer: [-1, 1]. Sine values are bounded between -1 and 1.

Flashcard 14: What is the range of the cosine function?

Answer: [-1, 1]. Cosine values are bounded between -1 and 1.

Flashcard 15: What is the secant of a 60-degree angle?

Answer:

1. Secant is the reciprocal of cosine; $\cos 60° = \frac{1}{2}$.

Flashcard 16: What is the value of $\text{cos}^2 45^\text{o}$?

Answer: $\frac{1}{2}$. Square of $\frac{\sqrt{2}}{2}$ equals $\frac{1}{2}$.

Flashcard 17: Find the exact value of $\text{sin} 30^\text{o}$.

Answer: $\frac{1}{2}$. In a 30-60-90 triangle, the shortest side is half the hypotenuse.

Flashcard 18: What is the sine of $45^\text{o}$?

Answer: $\frac{\text{sqrt}(2)}{2}$. Standard value for 45° in the unit circle.

Flashcard 19: What is the cosine of $0^\text{o}$?

Answer:

1. At 0°, the x-coordinate on the unit circle is 1.

Flashcard 20: State the half angle formula for cosine.

Answer: $\cos(\frac{\theta}{2}) = \sqrt{\frac{1 + \cos(\theta)}{2}}$. Formula for cosine of half angle.

Flashcard 21: State the Pythagorean identity for sine and cosine.

Answer: $\text{sin}^2 \theta + \text{cos}^2 \theta = 1$. Fundamental identity derived from the unit circle.

Flashcard 22: What is the period of the sine function?

Answer: $2\pi$. Sine completes one cycle every $2\pi$ radians.

Flashcard 23: What is the value of $\text{cos}^2 45^\text{o}$?

Answer: $\frac{1}{2}$. Square of $\frac{\sqrt{2}}{2}$ equals $\frac{1}{2}$.

Flashcard 24: Identify the reciprocal of cosine.

Answer: Secant (sec). Secant is defined as $\frac{1}{\cos}$.

Flashcard 25: Find the value of $\text{tan}^2 45^\text{o}$.

Answer:

1. Square of $\tan 45° = 1$ is 1.

Flashcard 26: State the angle addition formula for sine.

Answer: $\text{sin}(A + B) = \text{sin}A \text{cos}B + \text{cos}A \text{sin}B$. Formula for sine of sum of two angles.

Flashcard 27: Find $\text{cos}(2\theta)$ if $\text{cos}\theta = \frac{1}{2}$ and $\text{sin}\theta = \frac{\text{sqrt}(3)}{2}$.

Answer: $\text{cos}(2\theta) = -\frac{1}{2}$. Using double angle formula with given values.

Flashcard 28: What is the sine of $90^\text{o}$?

Answer:

1. At 90°, the y-coordinate on the unit circle is 1.

Flashcard 29: What is the cosine of $45^\text{o}$?

Answer: $\frac{\text{sqrt}(2)}{2}$. Standard value for 45° in the unit circle.

Flashcard 30: What is the tangent of $60^\text{o}$?

Answer: $\text{tan } 60^\text{o} = \frac{\text{sin } 60^\text{o}}{\text{cos } 60^\text{o}} = \frac{\frac{\text{sqrt}(3)}{2}}{\frac{1}{2}} = \text{sqrt}(3)$. Using the definition $\tan = \frac{\sin}{\cos}$.

Flashcard 31: Identify the cofunction identity for cosine.

Answer: $\text{cos}(90^\text{o} - \theta) = \text{sin}(\theta)$. Complementary angle relationship for cosine.

Flashcard 32: What is the sine of a $45^\text{°}$ angle in a right triangle?

Answer: $\frac{\text{√}2}{2}$. In a 45-45-90 triangle, opposite and adjacent sides are equal.

Flashcard 33: Identify the cofunction identity for sine.

Answer: $\text{sin}(90^\text{o} - \theta) = \text{cos}(\theta)$. Complementary angle relationship for sine.

Flashcard 34: What is the cosine of $90^\text{o}$?

Answer:

1. At 90°, the x-coordinate on the unit circle is 0.

Flashcard 35: What is the reciprocal of cosine?

Answer: Secant. Secant function is defined as $\sec \theta = \frac{1}{\cos \theta}$.

Flashcard 36: What is the period of the tangent function?

Answer: $\text{π}$. Tangent completes one cycle every $\pi$ radians.

Flashcard 37: What is the range of the cosine function?

Answer: [-1, 1]. Cosine values are bounded between -1 and 1.

Flashcard 38: Find $\text{sin}(30^\text{o})$ using cofunction identity.

Answer: $\text{cos}(60^\text{o}) = \frac{1}{2}$. Using $\sin(90° - 60°) = \cos 60°$.

Flashcard 39: Find $\sin(2\theta)$ if $\cos\theta = \frac{1}{2}$ and $\sin\theta = \frac{\sqrt{3}}{2}$.

Answer: $\sin(2\theta) = \sqrt{3}$. Using double angle formula with given values.

Flashcard 40: What is the tangent of $30^\text{o}$?

Answer: $\frac{1}{\text{sqrt}(3)}$. Using the 30-60-90 triangle ratios.

Flashcard 41: What is the tangent of $60^\text{o}$?

Answer: $\text{tan } 60^\text{o} = \frac{\text{sin } 60^\text{o}}{\text{cos } 60^\text{o}} = \frac{\frac{\text{sqrt}(3)}{2}}{\frac{1}{2}} = \text{sqrt}(3)$. Using the definition $\tan = \frac{\sin}{\cos}$.

Flashcard 42: State the Pythagorean identity for sine and cosine.

Answer: $\text{sin}^2 \theta + \text{cos}^2 \theta = 1$. Fundamental identity derived from the unit circle.

Flashcard 43: What is the tangent of $45^\text{o}$?

Answer:

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

Flashcard 44: Convert 180 degrees to radians.

Answer: $\text{π}$ radians. Use the conversion factor $\frac{\pi}{180}$.

Flashcard 45: What is the sine of $90^\text{o}$?

Answer:

1. At 90°, the y-coordinate on the unit circle is 1.

Flashcard 46: What is the cosine of $45^\text{o}$?

Answer: $\frac{\text{sqrt}(2)}{2}$. Standard value for 45° in the unit circle.

Flashcard 47: What is the secant of a 60-degree angle?

Answer:

1. Secant is the reciprocal of cosine; $\cos 60° = \frac{1}{2}$.

Flashcard 48: State the angle addition formula for tangent.

Answer: $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$. Formula for tangent of sum of two angles.

Flashcard 49: What is the sine of a $45^\text{°}$ angle in a right triangle?

Answer: $\frac{\text{√}2}{2}$. In a 45-45-90 triangle, opposite and adjacent sides are equal.

Flashcard 50: What is the sine of $60^\text{o}$?

Answer: $\frac{\sqrt{3}}{2}$. Standard value for 60° in the unit circle.

Flashcard 51: What is the reciprocal of cosine?

Answer: Secant. Secant function is defined as $\sec \theta = \frac{1}{\cos \theta}$.

Flashcard 52: Identify the reciprocal of cosine.

Answer: Secant (sec). Secant is defined as $\frac{1}{\cos}$.

Flashcard 53: What is the cosine of $90^\text{o}$?

Answer:

1. At 90°, the x-coordinate on the unit circle is 0.

Flashcard 54: What is the value of $\text{sin}^2 45^\text{o}$?

Answer: $\frac{1}{2}$. Square of $\frac{\sqrt{2}}{2}$ equals $\frac{1}{2}$.

Flashcard 55: State the angle addition formula for cosine.

Answer: $\text{cos}(A + B) = \text{cos}A \text{cos}B - \text{sin}A \text{sin}B$. Formula for cosine of sum of two angles.

Flashcard 56: Identify the cosine of a 0-degree angle.

Answer:

1. At 0°, the adjacent side equals the hypotenuse.

Flashcard 57: State the angle addition formula for cosine.

Answer: $\text{cos}(A + B) = \text{cos}A \text{cos}B - \text{sin}A \text{sin}B$. Formula for cosine of sum of two angles.

Flashcard 58: What is the cosine of $30^\text{o}$?

Answer: $\frac{\text{sqrt}(3)}{2}$. Standard value for 30° in the unit circle.

Flashcard 59: What is the period of the cosine function?

Answer: $2\pi$. Cosine completes one cycle every $2\pi$ radians.

Flashcard 60: Identify the cofunction identity for cosine.

Answer: $\text{cos}(90^\text{o} - \theta) = \text{sin}(\theta)$. Complementary angle relationship for cosine.

Flashcard 61: State the double angle formula for sine.

Answer: $\sin(2\theta) = 2 \sin(\theta) \cos(\theta)$. Formula for sine of double angle.

Flashcard 62: State the formula for the area of a triangle using sine.

Answer: $\frac{1}{2}ab \sin C$. Uses two sides and the included angle between them.

Flashcard 63: What is the sine of $30^\text{o}$?

Answer: $\frac{1}{2}$. Standard value for 30° in the unit circle.

Flashcard 64: What is the formula for the tangent of an angle in a right triangle?

Answer: $\text{tan} \theta = \frac{\text{opp}}{\text{adj}}$. Tangent equals opposite side divided by adjacent side.

Flashcard 65: State the double angle formula for cosine.

Answer: $\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$. Formula for cosine of double angle.

Flashcard 66: Find the exact value of $\text{sin} 30^\text{o}$.

Answer: $\frac{1}{2}$. In a 30-60-90 triangle, the shortest side is half the hypotenuse.

Flashcard 67: State the Pythagorean identity for sine and cosine.

Answer: $\text{sin}^2 \theta + \text{cos}^2 \theta = 1$. Fundamental identity derived from the Pythagorean theorem.

Flashcard 68: Identify the reciprocal of tangent.

Answer: Cotangent (cot). Cotangent is defined as $\frac{1}{\tan}$.

Flashcard 69: What is the formula for the tangent of an angle in a right triangle?

Answer: $\text{tan} \theta = \frac{\text{opp}}{\text{adj}}$. Tangent equals opposite side divided by adjacent side.

Flashcard 70: What is the value of $\text{sin}^2 45^\text{o}$?

Answer: $\frac{1}{2}$. Square of $\frac{\sqrt{2}}{2}$ equals $\frac{1}{2}$.

Flashcard 71: State the double angle formula for cosine.

Answer: $\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$. Formula for cosine of double angle.

Flashcard 72: What is the period of the tangent function?

Answer: $\text{π}$. Tangent completes one cycle every $\pi$ radians.

Flashcard 73: State the Pythagorean identity involving sine and cosine.

Answer: $\text{sin}^2\theta + \text{cos}^2\theta = 1$. Fundamental trigonometric identity derived from the unit circle.

Flashcard 74: Identify the reciprocal function of sine.

Answer: Cosecant (csc). Since $\sin\theta = \frac{1}{\csc\theta}$, cosecant is sine's reciprocal.

Flashcard 75: Identify the cosine of a 0-degree angle.

Answer:

1. At 0°, the adjacent side equals the hypotenuse.

Flashcard 76: Find $\text{cos}(60^\text{o})$ using cofunction identity.

Answer: $\text{sin}(30^\text{o}) = \frac{1}{2}$. Using $\cos(90° - 30°) = \sin 30°$.

Flashcard 77: What is the period of the cosine function?

Answer: $2\text{π}$. Cosine completes one cycle every $2\pi$ radians.

Flashcard 78: State the formula for the area of a triangle using sine.

Answer: $\frac{1}{2}ab \sin C$. Uses two sides and the included angle between them.

Flashcard 79: State the half angle formula for cosine.

Answer: $\cos(\frac{\theta}{2}) = \sqrt{\frac{1 + \cos(\theta)}{2}}$. Formula for cosine of half angle.

Flashcard 80: What is the range of the sine function?

Answer: [-1, 1]. Sine values are bounded between -1 and 1.

Flashcard 81: What is the cosine of $0^\text{o}$?

Answer:

1. At 0°, the x-coordinate on the unit circle is 1.

Flashcard 82: Convert 180 degrees to radians.

Answer: $\pi$ radians. Use the conversion factor $\frac{\pi}{180}$.

Flashcard 83: State the half angle formula for sine.

Answer: $\text{sin}(\frac{\theta}{2}) = \text{sqrt}(\frac{1 - \text{cos}(\theta)}{2})$. Formula for sine of half angle.

Flashcard 84: What is the tangent of $30^\text{o}$?

Answer: $\frac{1}{\sqrt{3}}$. Using the 30-60-90 triangle ratios.

Flashcard 85: What is the sine of a 90-degree angle?

Answer:

1. At 90°, the opposite side equals the hypotenuse in a right triangle.

Flashcard 86: What is the period of the sine function?

Answer: $2\text{π}$. Sine completes one cycle every $2\pi$ radians.

Flashcard 87: State the angle addition formula for sine.

Answer: $\text{sin}(A + B) = \text{sin}A \text{cos}B + \text{cos}A \text{sin}B$. Formula for sine of sum of two angles.

Flashcard 88: State the half angle formula for sine.

Answer: $\sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1 - \cos(\theta)}{2}}$. Formula for sine of half angle.

Flashcard 89: State the half angle formula for tangent.

Answer: $\text{tan}(\frac{\theta}{2}) = \text{sqrt}(\frac{1 - \text{cos}(\theta)}{1 + \text{cos}(\theta)})$. Formula for tangent of half angle.

Flashcard 90: Find $\text{sin}(30^\text{o})$ using cofunction identity.

Answer: $\text{cos}(60^\text{o}) = \frac{1}{2}$. Using $\sin(90° - 60°) = \cos 60°$.

Flashcard 91: State the double angle formula for sine.

Answer: $\sin(2\theta) = 2 \sin(\theta) \cos(\theta)$. Formula for sine of double angle.

Flashcard 92: Find $\cos(2\theta)$ if $\cos \theta = \frac{1}{2}$ and $\sin \theta = \frac{\sqrt{3}}{2}$.

Answer: $\cos(2\theta) = -\frac{1}{2}$. Using double angle formula with given values.

Flashcard 93: State the half angle formula for tangent.

Answer: $\tan(\frac{\theta}{2}) = \sqrt{\frac{1 - \cos(\theta)}{1 + \cos(\theta)}}$. Formula for tangent of half angle.

Flashcard 94: What is the cosine of $60^\text{o}$?

Answer: $\frac{1}{2}$. Standard value for 60° in the unit circle.

Flashcard 95: Find the cotangent of a 45-degree angle.

Answer:

1. Since $\tan 45° = 1$, cotangent is the reciprocal.

Flashcard 96: State the double angle formula for tangent.

Answer: $\text{tan}(2\theta) = \frac{2\text{tan}(\theta)}{1-\text{tan}^2(\theta)}$. Formula for tangent of double angle.

Flashcard 97: What is the tangent of $45^\text{o}$?

Answer:

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

Flashcard 98: Find the cotangent of a 45-degree angle.

Answer:

1. Since $\tan 45° = 1$, cotangent is the reciprocal.

Flashcard 99: Find $\sin(2\theta)$ if $\cos\theta = \frac{1}{2}$ and $\sin\theta = \frac{\sqrt{3}}{2}$.

Answer: $\sin(2\theta) = \sqrt{3}$. Using double angle formula with given values.

Flashcard 100: What is the cosine of $30^\text{o}$?

Answer: $\frac{\text{sqrt}(3)}{2}$. Standard value for 30° in the unit circle.