Exact Values of Sine, Cosine and Tangent · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Angles you just know

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. What is tan 45 degrees?

    Answer: ______________

  2. What is cos 30 degrees?

    • root 3 over 2
    • 1/2
    • root 2 over 2

  3. What is sin 30 degrees?

    • 1/2
    • 1/4
    • 1

  4. Tan 45 degrees equals 1 because the two legs of the triangle are equal.

    Circle one:   True   False

  5. Halving an equilateral triangle of side 12 gives a right angled triangle with hypotenuse 12. What is the leg adjacent to the 60 degree angle?

    • 12
    • 6
    • 6 root 3

  6. Which of these should be left in surd form rather than rounded?

    • Sin 60 degrees
    • Sin 30 degrees
    • Tan 45 degrees

  7. An equilateral triangle with side length 8 is cut in half down the middle. What is the length of the shortest side of each half?

    Answer: ______________

  8. Which of these values is undefined?

    • tan 90 degrees
    • tan 45 degrees
    • sin 30 degrees

  9. A right angled triangle has a 45 degree angle and the leg adjacent to that angle is 9 cm long. How long is the side opposite the angle, in cm?

    Answer: ______________

  10. A right angled triangle has a 45 degree angle and the leg adjacent to that angle is 7 cm long. How long is the side opposite the angle, in cm?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Angles you just know W1-mt_SNJEbXYOrR-s1

  1. 1 · Tan 45 is opposite over adjacent, and the two legs of a 45-45-90 triangle are equal, so the answer is 1.
  2. root 3 over 2 · Cos 30 is the long leg over the hypotenuse in a halved equilateral triangle, which is root 3 over 2.
  3. 1/2 · Sin 30 is one half, the first of the must-know trio.
  4. True · Opposite over adjacent with equal legs gives exactly 1.
  5. 6 · The leg adjacent to 60 degrees is the short leg, half the original side, so 12 becomes 6.
  6. Sin 60 degrees · Sin 60 is root 3 over 2, which never comes out neat.
  7. 4 · The cut splits one side of 8 into two equal halves of 4, and the shortest side of each half is 4.
  8. tan 90 degrees · Tan 90 is y over x at the point (0, 1), which is 1 over 0, undefined.
  9. 9 · Tan 45 is 1, so opposite equals adjacent, which is 9 cm.
  10. 7 · Tan 45 is 1, so opposite equals adjacent, which is 7 cm.
Worksheet · LightMySky