AP Precalculus Flashcards: Sine Cosine And Tangent

Study Sine Cosine And Tangent in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Sine Cosine And Tangent

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QUESTION
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Find tan(π4)\text{tan}(\frac{\pi}{4}) using the unit circle.

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

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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.

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Flashcard 1: Find tan(π4)\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 cos(\textpi)\text{cos}(\text{\textpi})?

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

Flashcard 3: What is the period of the cosine function?

Answer: 2π2\pi. Cosine repeats its values every 2π2\pi radians.

Flashcard 4: What is the cosine of 60o60^\text{o}?

Answer: 12\frac{1}{2}. From the 30°60°90°30°-60°-90° triangle or unit circle.

Flashcard 5: What is the phase shift of y=cos(x+π6)y = \cos(x + \frac{\pi}{6})?

Answer: π6\frac{\pi}{6} to the left. A positive value inside parentheses shifts the graph left.

Flashcard 6: What is the phase shift of y=sin(xπ4)y = \sin(x - \frac{\pi}{4})?

Answer: π4\frac{\pi}{4} to the right. A negative value inside parentheses shifts the graph right.

Flashcard 7: Convert π3\frac{\pi}{3} radians to degrees.

Answer: 6060^\circ. Use the formula degrees=radians×180π\text{degrees} = \text{radians} \times \frac{180^\circ}{\pi}

Flashcard 8: What is the period of the tangent function?

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

Flashcard 9: What is the reciprocal of sine?

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

Flashcard 10: What is the tangent of 45o45^\text{o}?

Answer:

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

Flashcard 11: Find the tangent of angle CC if sin(C)=35\text{sin}(C) = \frac{3}{5} and CC is in Quadrant I.

Answer: 34\frac{3}{4}. First find cosC=45\cos C = \frac{4}{5}, then tanC=sinCcosC\tan C = \frac{\sin C}{\cos C}.

Flashcard 12: 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 13: What is the general solution for sin(x)=0\text{sin}(x) = 0?

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

Flashcard 14: Find the cosine of angle BB if sin(B)=513\text{sin}(B) = \frac{5}{13} and BB is in Quadrant I.

Answer: 1213\frac{12}{13}. Use sin2B+cos2B=1\sin^2 B + \cos^2 B = 1 to find cosB=1(513)2\cos B = \sqrt{1 - (\frac{5}{13})^2}.

Flashcard 15: Convert 45o45^\text{o} to radians.

Answer: \textpi4\frac{\text{\textpi}}{4}. Use the formula radians=degrees×π180°\text{radians} = \text{degrees} \times \frac{\pi}{180°}.

Flashcard 16: What is the reference angle for 210o210^\text{o}?

Answer: 30o30^\text{o}. Reference angle is 210°180°=30°210° - 180° = 30°.

Flashcard 17: What is the phase shift of y=sin(xπ4)y = \sin(x - \frac{\pi}{4})?

Answer: π4\frac{\pi}{4} to the right. A negative value inside parentheses shifts the graph right.

Flashcard 18: 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 19: Which quadrant has positive sine and cosine values?

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

Flashcard 20: What is the value of tan(π)\tan(\pi)?

Answer:

  1. Since tan(π)=sin(π)cos(π)=01\tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1}.

Flashcard 21: What is the phase shift of y=cos(x+π6)y = \cos(x + \frac{\pi}{6})?

Answer: π6\frac{\pi}{6} to the left. A positive value inside parentheses shifts the graph left.

Flashcard 22: What is the tangent of an angle in Quadrant IV?

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

Flashcard 23: Find cos(π3)\cos\left(\frac{\pi}{3}\right) using the unit circle.

Answer: 12\frac{1}{2}. This is a standard angle value on the unit circle.

Flashcard 24: What is the reciprocal of tangent?

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

Flashcard 25: What is the tangent of 0o0^\text{o}?

Answer:

  1. Since tan(0°)=sin(0°)cos(0°)=01\tan(0°) = \frac{\sin(0°)}{\cos(0°)} = \frac{0}{1}.

Flashcard 26: What is the sine of 30o30^\text{o}?

Answer: 12\frac{1}{2}. From the 30°60°90°30°-60°-90° triangle or unit circle.

Flashcard 27: Find sin(π6)\sin\left(\frac{\pi}{6}\right) using the unit circle.

Answer: 12\frac{1}{2}. This is a standard angle value on the unit circle.

Flashcard 28: 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 29: Find cos(π3)\cos\left(\frac{\pi}{3}\right) using the unit circle.

Answer: 12\frac{1}{2}. This is a standard angle value on the unit circle.

Flashcard 30: What is the period of the tangent function?

Answer: \textpi\text{\textpi}. Tangent repeats its values every π\pi radians.

Flashcard 31: What is the reference angle for 7π6\frac{7\pi}{6}?

Answer: π6\frac{\pi}{6}. Reference angle is 7π6π=π6\frac{7\pi}{6} - \pi = \frac{\pi}{6}.

Flashcard 32: Which quadrant has positive sine and cosine values?

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

Flashcard 33: What is the reciprocal of cosine?

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

Flashcard 34: What is the amplitude of y=3sin(x)y = 3\text{sin}(x)?

Answer:

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

Flashcard 35: What is the general solution for sin(x)=0\sin(x) = 0?

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

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

Answer: 2π2\pi. Sine repeats its values every 2π2\pi radians.

Flashcard 37: What is the sine of 90o90^\text{o}?

Answer:

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

Flashcard 38: What is the tangent of 0o0^\text{o}?

Answer:

  1. Since tan(0)=sin(0)cos(0)=01\tan(0^\circ) = \frac{\sin(0^\circ)}{\cos(0^\circ)} = \frac{0}{1}.

Flashcard 39: 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.

Flashcard 40: What is the value of cos(π)\cos(\pi)?

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

Flashcard 41: 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 42: What is the reciprocal of tangent?

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

Flashcard 43: Find the sine of angle AA if cos(A)=35\text{cos}(A) = \frac{3}{5} and AA is in Quadrant I.

Answer: 45\frac{4}{5}. Use sin2A+cos2A=1\sin^2 A + \cos^2 A = 1 to find sinA=1(35)2\sin A = \sqrt{1 - (\frac{3}{5})^2}.

Flashcard 44: State the Pythagorean identity involving sine and cosine.

Answer: sin2θ+cos2θ=1\text{sin}^2 \theta + \text{cos}^2 \theta = 1. This comes from the Pythagorean theorem applied to the unit circle.

Flashcard 45: What is the reciprocal of cosine?

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

Flashcard 46: Convert \textpi3\frac{\text{\textpi}}{3} radians to degrees.

Answer: 60o60^\text{o}. Use the formula degrees=radians×180°π\text{degrees} = \text{radians} \times \frac{180°}{\pi}.

Flashcard 47: What is the tangent of an angle in Quadrant IV?

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

Flashcard 48: What is the tangent of 45o45^\text{o}?

Answer:

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

Flashcard 49: What is the cosine of 0o0^\text{o}?

Answer:

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

Flashcard 50: What is the value of sin(\textpi)\text{sin}(\text{\textpi})?

Answer:

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

Flashcard 51: What is the amplitude of y=2cos(x)y = -2\text{cos}(x)?

Answer:

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

Flashcard 52: Find tan(π4)\tan(\frac{\pi}{4}) using the unit circle.

Answer:

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

Flashcard 53: What is the amplitude of y=2cos(x)y = -2\text{cos}(x)?

Answer:

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

Flashcard 54: Find the tangent of angle CC if sin(C)=35\text{sin}(C) = \frac{3}{5} and CC is in Quadrant I.

Answer: 34\frac{3}{4}. First find cosC=45\cos C = \frac{4}{5}, then tanC=sinCcosC\tan C = \frac{\sin C}{\cos C}.

Flashcard 55: What is the period of the cosine function?

Answer: 2π2\pi. Cosine repeats its values every 2π2\pi radians.

Flashcard 56: What is the vertical shift of y=tan(x)+3y = \text{tan}(x) + 3?

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

Flashcard 57: What is the cosine of an angle in Quadrant III?

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

Flashcard 58: What is the period of the sine function?

Answer: 2π2\pi. Sine repeats its values every 2π2\pi radians.

Flashcard 59: Convert 45o45^\text{o} to radians.

Answer: \textpi4\frac{\text{\textpi}}{4}. Use the formula radians=degrees×π180°\text{radians} = \text{degrees} \times \frac{\pi}{180°}.

Flashcard 60: What is the value of tan(\textpi)\text{tan}(\text{\textpi})?

Answer:

  1. Since tan(π)=sin(π)cos(π)=01\tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1}.

Flashcard 61: What is the reciprocal of sine?

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

Flashcard 62: What is the reference angle for 7π6\frac{7\pi}{6}?

Answer: π6\frac{\pi}{6}. Reference angle is 7π6π=π6\frac{7\pi}{6} - \pi = \frac{\pi}{6}.

Flashcard 63: What is the cosine of an angle in Quadrant III?

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

Flashcard 64: Find the sine of angle AA if cos(A)=35\text{cos}(A) = \frac{3}{5} and AA is in Quadrant I.

Answer: 45\frac{4}{5}. Use sin2A+cos2A=1\sin^2 A + \cos^2 A = 1 to find sinA=1(35)2\sin A = \sqrt{1 - (\frac{3}{5})^2}.

Flashcard 65: What is the value of sin(\textpi)\text{sin}(\text{\textpi})?

Answer:

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

Flashcard 66: What is the sine of 30o30^\text{o}?

Answer: 12\frac{1}{2}. From the 30°60°90°30°-60°-90° triangle or unit circle.

Flashcard 67: What is the cosine of 0o0^\text{o}?

Answer:

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

Flashcard 68: What is the vertical shift of y=tan(x)+3y = \text{tan}(x) + 3?

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

Flashcard 69: What is the cosine of 60o60^\text{o}?

Answer: 12\frac{1}{2}. From the 30°60°90°30°-60°-90° triangle or unit circle.

Flashcard 70: What is the reference angle for 210o210^\text{o}?

Answer: 30o30^\text{o}. Reference angle is 210°180°=30°210° - 180° = 30°.

Flashcard 71: What is the amplitude of y=3sin(x)y = 3\text{sin}(x)?

Answer:

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

Flashcard 72: Find the cosine of angle BB if sin(B)=513\text{sin}(B) = \frac{5}{13} and BB is in Quadrant I.

Answer: 1213\frac{12}{13}. Use sin2B+cos2B=1\sin^2 B + \cos^2 B = 1 to find cosB=1(513)2\cos B = \sqrt{1 - (\frac{5}{13})^2}.

Flashcard 73: What is the sine of 90o90^\text{o}?

Answer:

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

Flashcard 74: State the Pythagorean identity involving sine and cosine.

Answer: sin2θ+cos2θ=1\text{sin}^2 \theta + \text{cos}^2 \theta = 1. This comes from the Pythagorean theorem applied to the unit circle.

Flashcard 75: 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.