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Flashcards · Maths · Further Trigonometry

Trigonometric Graphs and Exact Values

16 cards

  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.