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(4π) using the unit circle.
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ANSWER
This is a standard angle value on the unit circle.
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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.
All flashcards
Flashcard 1: Find tan(4π) using the unit circle.
Answer:
This is a standard angle value on the unit circle.
Flashcard 2: What is the value of cos(\textpi)?
Answer: -1. At π, the point is (−1,0) on the unit circle.
Flashcard 3: What is the period of the cosine function?
Answer: 2π. Cosine repeats its values every 2π radians.
Flashcard 4: What is the cosine of 60o?
Answer: 21. From the 30°−60°−90° triangle or unit circle.
Flashcard 5: What is the phase shift of y=cos(x+6π)?
Answer: 6π to the left. A positive value inside parentheses shifts the graph left.
Flashcard 6: What is the phase shift of y=sin(x−4π)?
Answer: 4π to the right. A negative value inside parentheses shifts the graph right.
Flashcard 7: Convert 3π radians to degrees.
Answer: 60∘. Use the formula degrees=radians×π180∘
Flashcard 8: What is the period of the tangent function?
Answer: π. Tangent repeats its values every π radians.
Flashcard 9: What is the reciprocal of sine?
Answer: Cosecant. Cosecant is sin(x)1.
Flashcard 10: What is the tangent of 45o?
Answer:
In a 45°−45°−90° triangle, opposite equals adjacent.
Flashcard 11: Find the tangent of angle C if sin(C)=53 and C is in Quadrant I.
Answer: 43. First find cosC=54, then tanC=cosCsinC.
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?
Answer: x=n\textpi, where n is an integer. Sine equals zero at integer multiples of π.
Flashcard 14: Find the cosine of angle B if sin(B)=135 and B is in Quadrant I.
Answer: 1312. Use sin2B+cos2B=1 to find cosB=1−(135)2.
Flashcard 15: Convert 45o to radians.
Answer: 4\textpi. Use the formula radians=degrees×180°π.
Flashcard 16: What is the reference angle for 210o?
Answer: 30o. Reference angle is 210°−180°=30°.
Flashcard 17: What is the phase shift of y=sin(x−4π)?
Answer: 4π 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)?
Answer:
Since tan(π)=cos(π)sin(π)=−10.
Flashcard 21: What is the phase shift of y=cos(x+6π)?
Answer: 6π 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(3π) using the unit circle.
Answer: 21. This is a standard angle value on the unit circle.
Flashcard 24: What is the reciprocal of tangent?
Answer: Cotangent. Cotangent is tan(x)1.
Flashcard 25: What is the tangent of 0o?
Answer:
Since tan(0°)=cos(0°)sin(0°)=10.
Flashcard 26: What is the sine of 30o?
Answer: 21. From the 30°−60°−90° triangle or unit circle.
Flashcard 27: Find sin(6π) using the unit circle.
Answer: 21. 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(3π) using the unit circle.
Answer: 21. This is a standard angle value on the unit circle.
Flashcard 30: What is the period of the tangent function?
Answer: \textpi. Tangent repeats its values every π radians.
Flashcard 31: What is the reference angle for 67π?
Answer: 6π. Reference angle is 67π−π=6π.
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 cos(x)1.
Flashcard 34: What is the amplitude of y=3sin(x)?
Answer:
The coefficient of the sine function is the amplitude.
Flashcard 35: What is the general solution for sin(x)=0?
Answer: x=nπ, where n is an integer. Sine equals zero at integer multiples of π.
Flashcard 36: What is the period of the sine function?
Answer: 2π. Sine repeats its values every 2π radians.
Flashcard 37: What is the sine of 90o?
Answer:
At 90°, the point is (0,1) on the unit circle.
Flashcard 38: What is the tangent of 0o?
Answer:
Since tan(0∘)=cos(0∘)sin(0∘)=10.
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)?
Answer: -1. At π, the point is (−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 tan(x)1.
Flashcard 43: Find the sine of angle A if cos(A)=53 and A is in Quadrant I.
Answer: 54. Use sin2A+cos2A=1 to find sinA=1−(53)2.
Flashcard 44: State the Pythagorean identity involving sine and cosine.
Answer: sin2θ+cos2θ=1. This comes from the Pythagorean theorem applied to the unit circle.
Flashcard 45: What is the reciprocal of cosine?
Answer: Secant. Secant is cos(x)1.
Flashcard 46: Convert 3\textpi radians to degrees.
Answer: 60o. Use the formula degrees=radians×π180°.
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 45o?
Answer:
In a 45°−45°−90° triangle, opposite equals adjacent.
Flashcard 49: What is the cosine of 0o?
Answer:
At 0°, the point is (1,0) on the unit circle.
Flashcard 50: What is the value of sin(\textpi)?
Answer:
At π, the point is (−1,0) on the unit circle.
Flashcard 51: What is the amplitude of y=−2cos(x)?
Answer:
The absolute value of the coefficient is the amplitude.
Flashcard 52: Find tan(4π) using the unit circle.
Answer:
This is a standard angle value on the unit circle.
Flashcard 53: What is the amplitude of y=−2cos(x)?
Answer:
The absolute value of the coefficient is the amplitude.
Flashcard 54: Find the tangent of angle C if sin(C)=53 and C is in Quadrant I.
Answer: 43. First find cosC=54, then tanC=cosCsinC.
Flashcard 55: What is the period of the cosine function?
Answer: 2π. Cosine repeats its values every 2π radians.
Flashcard 56: What is the vertical shift of y=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: 2π. Sine repeats its values every 2π radians.
Flashcard 59: Convert 45o to radians.
Answer: 4\textpi. Use the formula radians=degrees×180°π.
Flashcard 60: What is the value of tan(\textpi)?
Answer:
Since tan(π)=cos(π)sin(π)=−10.
Flashcard 61: What is the reciprocal of sine?
Answer: Cosecant. Cosecant is sin(x)1.
Flashcard 62: What is the reference angle for 67π?
Answer: 6π. Reference angle is 67π−π=6π.
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 A if cos(A)=53 and A is in Quadrant I.
Answer: 54. Use sin2A+cos2A=1 to find sinA=1−(53)2.
Flashcard 65: What is the value of sin(\textpi)?
Answer:
At π, the point is (−1,0) on the unit circle.
Flashcard 66: What is the sine of 30o?
Answer: 21. From the 30°−60°−90° triangle or unit circle.
Flashcard 67: What is the cosine of 0o?
Answer:
At 0°, the point is (1,0) on the unit circle.
Flashcard 68: What is the vertical shift of y=tan(x)+3?
Answer: 3 units up. Adding a constant outside the function shifts vertically.
Flashcard 69: What is the cosine of 60o?
Answer: 21. From the 30°−60°−90° triangle or unit circle.
Flashcard 70: What is the reference angle for 210o?
Answer: 30o. Reference angle is 210°−180°=30°.
Flashcard 71: What is the amplitude of y=3sin(x)?
Answer:
The coefficient of the sine function is the amplitude.
Flashcard 72: Find the cosine of angle B if sin(B)=135 and B is in Quadrant I.
Answer: 1312. Use sin2B+cos2B=1 to find cosB=1−(135)2.
Flashcard 73: What is the sine of 90o?
Answer:
At 90°, the point is (0,1) on the unit circle.
Flashcard 74: State the Pythagorean identity involving sine and cosine.
Answer: sin2θ+cos2θ=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.