# GRE Trigonometric Applications

> Essential trigonometry concepts and applications in coordinate geometry, including special angles and identities specific to GRE questions

- **Canonical URL:** https://flashcards.world/flashcards/sets/197eb59e-90f4-4b5c-b1fe-737b2b35908a/
- **Markdown URL:** https://flashcards.world/flashcards/sets/197eb59e-90f4-4b5c-b1fe-737b2b35908a.md
- **Level:** intermediate
- **Languages:** en → en
- **Total Cards:** 54

## Flashcards (54 Cards)

| # | Front (Term / Prompt) | Back (Definition / Answer) | Example | Multiple-Choice Options |
| :--- | :--- | :--- | :--- | :--- |
| 1 | What is the cosine of 120 degrees? | The cosine of 120 degrees is -1/2. |  |  |
| 2 | What is the cosine of 60 degrees? | The cosine of 60 degrees is 0.5. |  |  |
| 3 | What is the sine of 120 degrees? | The sine of 120 degrees is √3/2. |  |  |
| 4 | What is the value of cos(360 degrees)? | The value of cos(360 degrees) is 1. |  |  |
| 5 | What is the formula for converting radians to degrees? | Degrees = Radians × (180/π). |  |  |
| 6 | What is the amplitude of the tangent function? | The tangent function does not have an amplitude. |  |  |
| 7 | What is the cosine of 0 degrees? | The cosine of 0 degrees is 1. |  |  |
| 8 | What is the value of tan(45 degrees)? | The value of tan(45 degrees) is 1. |  |  |
| 9 | What is the sine of 90 degrees? | The sine of 90 degrees is 1. |  |  |
| 10 | What is the sine of 210 degrees? | The sine of 210 degrees is -1/2. |  |  |
| 11 | What is the formula for the sine of a sum of angles? | sin(a + b) = sin(a)cos(b) + cos(a)sin(b). |  |  |
| 12 | What is the sine of 330 degrees? | The sine of 330 degrees is -1/2. |  |  |
| 13 | What is the phase shift of the function y = cos(x + π/3)? | The phase shift is π/3 to the left. |  |  |
| 14 | What is the law of sines? | a/sin(A) = b/sin(B) = c/sin(C) for triangle ABC. |  |  |
| 15 | What is the tangent of 30 degrees? | The tangent of 30 degrees is 1/√3 or √3/3. |  |  |
| 16 | What is the cosine of an angle in the first quadrant? | The cosine is positive in the first quadrant. |  |  |
| 17 | What is the period of the cosine function? | The period of the cosine function is 2π. |  |  |
| 18 | What is the value of cos(180 degrees)? | The value of cos(180 degrees) is -1. |  |  |
| 19 | What is the value of tan(90 degrees)? | The value of tan(90 degrees is undefined. |  |  |
| 20 | What is the cosine of an angle in a right triangle? | The cosine is the ratio of the length of the adjacent side to the hypotenuse. |  |  |
| 21 | What is the reference angle for 300 degrees? | The reference angle for 300 degrees is 60 degrees. |  |  |
| 22 | What is the cosine of an angle in terms of the unit circle? | The cosine of an angle is the x-coordinate of the corresponding point on the unit circle. |  |  |
| 23 | What is the cosine of 30 degrees? | The cosine of 30 degrees is √3/2. |  |  |
| 24 | What is the relationship between sine and cosine for complementary angles? | sin(θ) = cos(90° - θ). |  |  |
| 25 | What is the sine of 30 degrees? | The sine of 30 degrees is 0.5. |  |  |
| 26 | What is the amplitude of the cosine function? | The amplitude of the cosine function is 1. |  |  |
| 27 | What is the relationship between the sides of a right triangle and trigonometric ratios? | sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. |  |  |
| 28 | What is the formula for the tangent of a sum of angles? | tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b)). |  |  |
| 29 | What is the period of the tangent function? | The period of the tangent function is π. |  |  |
| 30 | What is the value of sin(360 degrees)? | The value of sin(360 degrees) is 0. |  |  |
| 31 | What is the value of sin(90 degrees)? | The value of sin(90 degrees) is 1. |  |  |
| 32 | What is the vertical shift of the function y = cos(x) - 1? | The vertical shift is 1 unit down. |  |  |
| 33 | What is the reference angle for 150 degrees? | The reference angle for 150 degrees is 30 degrees. |  |  |
| 34 | What is the vertical shift of the function y = sin(x) + 2? | The vertical shift is 2 units up. |  |  |
| 35 | What is the cosine of 330 degrees? | The cosine of 330 degrees is √3/2. |  |  |
| 36 | What is the cosine of 210 degrees? | The cosine of 210 degrees is -√3/2. |  |  |
| 37 | What is the cosine of an angle in the third quadrant? | The cosine is negative in the third quadrant. |  |  |
| 38 | What is the tangent of 60 degrees? | The tangent of 60 degrees is √3. |  |  |
| 39 | What is the cosine of 45 degrees? | The cosine of 45 degrees is √2/2. |  |  |
| 40 | What is the amplitude of the sine function? | The amplitude of the sine function is 1. |  |  |
| 41 | What is the Pythagorean identity involving sine and cosine? | sin²(θ) + cos²(θ) = 1. |  |  |
| 42 | What is the value of sin(180 degrees)? | The value of sin(180 degrees) is 0. |  |  |
| 43 | What is the formula for converting degrees to radians? | Radians = Degrees × (π/180). |  |  |
| 44 | What is the sine of an angle in a right triangle? | The sine is the ratio of the length of the opposite side to the hypotenuse. |  |  |
| 45 | What is the sine of an angle in the second quadrant? | The sine is positive in the second quadrant. |  |  |
| 46 | What is the sine of an angle in terms of the unit circle? | The sine of an angle is the y-coordinate of the corresponding point on the unit circle. |  |  |
| 47 | What is the reference angle for 240 degrees? | The reference angle for 240 degrees is 60 degrees. |  |  |
| 48 | What is the tangent of an angle in a right triangle? | The tangent is the ratio of the length of the opposite side to the adjacent side. |  |  |
| 49 | What is the phase shift of the function y = sin(x - π/2)? | The phase shift is π/2 to the right. |  |  |
| 50 | What is the sine of an angle in the fourth quadrant? | The sine is negative in the fourth quadrant. |  |  |
| 51 | What is the period of the sine function? | The period of the sine function is 2π. |  |  |
| 52 | What is the law of cosines? | c² = a² + b² - 2ab*cos(C) for triangle ABC. |  |  |
| 53 | What is the formula for the cosine of a sum of angles? | cos(a + b) = cos(a)cos(b) - sin(a)sin(b). |  |  |
| 54 | What is the sine of 45 degrees? | The sine of 45 degrees is √2/2. |  |  |

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