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Flashcards · Maths

Further Trigonometry

80 cards from 5 lessons

  1. What is the period of \(y = \sin x\)?

    \(360^\circ\).

  2. What is the period of \(y = \tan x\)?

    \(180^\circ\).

  3. What are the maximum and minimum values of \(y = \cos x\)?

    1 and \(-1\).

  4. Where does \(y = \sin x\) cross the \(x\)-axis between \(0^\circ\) and \(360^\circ\)?

    At \(0^\circ\), \(180^\circ\) and \(360^\circ\).

  5. Where does \(y = \cos x\) cross the \(x\)-axis between \(0^\circ\) and \(360^\circ\)?

    At \(90^\circ\) and \(270^\circ\).

  6. Where are the asymptotes of \(y = \tan x\) between \(0^\circ\) and \(360^\circ\)?

    At \(x = 90^\circ\) and \(x = 270^\circ\).

  7. What is \(\cos 0^\circ\)?

    1.

  8. What is \(\sin 90^\circ\)?

    1.

  9. What is \(\tan 45^\circ\)?

    1.

  10. What is the second solution of \(\sin x = k\) if the first is \(x\)?

    \(180^\circ - x\).

  11. What is the second solution of \(\cos x = k\) if the first is \(x\)?

    \(360^\circ - x\).

  12. How many solutions does \(\sin x = \dfrac{1}{2}\) have between \(0^\circ\) and \(360^\circ\)?

    Two, \(30^\circ\) and \(150^\circ\).

  13. What is \(\cos 120^\circ\)?

    \(-\dfrac{1}{2}\).

  14. Does \(\sin x = 1.5\) have a solution?

    No, because sine is never greater than 1.

  15. Where do the sine and cosine graphs cross between \(0^\circ\) and \(90^\circ\)?

    At \(45^\circ\).

  16. How is the cosine graph related to the sine graph?

    It is the sine graph translated \(90^\circ\) to the left.

  17. What is the sine rule for finding a side?

    \(\dfrac{a}{\sin A} = \dfrac{b}{\sin B}\).

  18. What is the sine rule for finding an angle?

    \(\dfrac{\sin A}{a} = \dfrac{\sin B}{b}\).

  19. What is a matching pair?

    A side and its opposite angle.

  20. Which side is opposite angle \(C\)?

    Side \(c\).

  21. When do you use the sine rule?

    When you have a matching pair and one other side or angle.

  22. When do you use the cosine rule instead?

    With two sides and the included angle, or three sides.

  23. What is \(\sin 30^\circ\)?

    \(\dfrac{1}{2}\).

  24. What is \(\sin 45^\circ\)?

    \(\dfrac{\sqrt{2}}{2}\).

  25. What is \(\sin 60^\circ\)?

    \(\dfrac{\sqrt{3}}{2}\).

  26. Which angle is opposite the longest side?

    The largest angle.

  27. What do the angles in a triangle add up to?

    \(180^\circ\).

  28. If two angles are \(30^\circ\) and \(45^\circ\), what is the third?

    \(105^\circ\).

  29. What does the sine rule say about the ratio of side to sine?

    It is the same for all three sides.

  30. How do you rearrange to make \(b\) the subject?

    \(b = \dfrac{a \sin B}{\sin A}\).

  31. Should you label the triangle first?

    Yes, write the letters on a sketch.

  32. What should you write before rearranging?

    The sine rule with the numbers in.

  33. What is the cosine rule for a side?

    \(a^2 = b^2 + c^2 - 2bc\cos A\).

  34. What is the cosine rule for an angle?

    \(\cos A = \dfrac{b^2 + c^2 - a^2}{2bc}\).

  35. When do you use the cosine rule?

    With two sides and the included angle, or with three sides.

  36. Which side is \(a\) in the formula?

    The side opposite angle \(A\).

  37. What is \(\cos 60^\circ\)?

    \(\dfrac{1}{2}\).

  38. What is \(\cos 120^\circ\)?

    \(-\dfrac{1}{2}\).

  39. What is \(\cos 90^\circ\)?

    0.

  40. What does the cosine rule become when \(A = 90^\circ\)?

    Pythagoras' theorem.

  41. What does a negative cosine tell you about the angle?

    It is obtuse.

  42. Which angle is the largest in a triangle?

    The one opposite the longest side.

  43. What is \(\cos 30^\circ\)?

    \(\dfrac{\sqrt{3}}{2}\).

  44. What is \(\cos 45^\circ\)?

    \(\dfrac{\sqrt{2}}{2}\).

  45. Which step comes before the square root when finding a side?

    Finding \(a^2\).

  46. Is the sine rule or cosine rule used for three sides?

    The cosine rule.

  47. What should you write before simplifying?

    The rule with the numbers substituted.

  48. What do the angles of a triangle add up to?

    \(180^\circ\).

  49. What is the area of a triangle given two sides and the included angle?

    \(\dfrac{1}{2}ab\sin C\).

  50. Which angle must be used in the formula?

    The angle between the two sides.

  51. Why is the formula \(\dfrac{1}{2}ab\sin C\)?

    The height is \(b\sin C\), so area is half base times height.

  52. What is \(\sin 30^\circ\)?

    \(\dfrac{1}{2}\).

  53. What is \(\sin 60^\circ\)?

    \(\dfrac{\sqrt{3}}{2}\).

  54. What is \(\sin 90^\circ\)?

    1.

  55. What does the area become if \(C = 90^\circ\)?

    \(\dfrac{1}{2}ab\).

  56. How do you find the angle from the area?

    \(\sin C = \dfrac{2 \times \text{Area}}{ab}\).

  57. What is a segment of a circle?

    The part between a chord and an arc.

  58. What is the area of a segment?

    Sector minus triangle.

  59. What is the area of a sector?

    \(\dfrac{\theta}{360} \times \pi r^2\).

  60. What is the area of the triangle in a sector with radius \(r\)?

    \(\dfrac{1}{2}r^2\sin\theta\).

  61. What is the second solution of \(\sin C = \dfrac{1}{2}\)?

    \(150^\circ\).

  62. What are the units of area?

    Square units, such as cm\(^2\).

  63. What does exact mean?

    Leaving the answer in surds and \(\pi\).

  64. Can you use any two sides?

    Yes, with the angle between them.

  65. What is the length of a space diagonal of a cuboid?

    \(\sqrt{l^2 + w^2 + h^2}\).

  66. What is the base diagonal of a 4 cm by 3 cm rectangle?

    5 cm.

  67. What is the angle between a line and a plane?

    The angle between the line and its shadow on the plane.

  68. Where is the apex of a square-based pyramid?

    Directly above the centre of the base.

  69. What is the length of the diagonal of a square with side 6 cm?

    \(6\sqrt{2}\) cm.

  70. What do you do first in a 3D problem?

    Draw a right-angled triangle on its own.

  71. What should you mark on the triangle?

    The right angle and the known lengths.

  72. What does \(\tan\theta = 1\) mean?

    \(\theta = 45^\circ\).

  73. Which trig ratio uses opposite and adjacent?

    Tangent.

  74. Which rule is used if there is no right angle?

    The sine rule or the cosine rule.

  75. What is \(\sqrt{48}\) in simplest form?

    \(4\sqrt{3}\).

  76. Why keep surds until the end?

    To give an exact answer and avoid rounding errors.

  77. What is \(\sin 30^\circ\)?

    \(\dfrac{1}{2}\).

  78. What is the space diagonal of a cube with edge 1?

    \(\sqrt{3}\).

  79. How many right-angled triangles are needed for a space diagonal?

    Two.

  80. Is the space diagonal longer than the edges?

    Yes.