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Trigonometric Functions Practice Problems

Use SOH CAH TOA for triangles and the unit circle for every other angle. For angles outside the first quadrant, find the reference angle and attach the right sign.

  1. 1.

    A right triangle has opposite side 3, adjacent side 4 and hypotenuse 5. Find .

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    Opposite over hypotenuse: .

  2. 2.

    For the same 3-4-5 triangle, find .

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    Opposite over adjacent: .

  3. 3.

    Find .

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    .

  4. 4.

    Find .

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    .

  5. 5.

    Find . Type square roots as sqrt( ).

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    .

  6. 6.

    Find .

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    Quadrant II, reference angle , cosine negative: .

  7. 7.

    Find .

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    Quadrant II, reference angle , sine positive: .

  8. 8.

    Find .

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    Quadrant II, tangent negative: .

  9. 9.

    Find .

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    Quadrant III, reference angle , cosine negative: .

  10. 10.

    Find .

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    , and , so 2.

  11. 11.

    If and is in quadrant II, find .

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    ; cosine is negative in quadrant II.

  12. 12.

    In which quadrant is and ? Type I, II, III or IV.

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    Only tangent is positive in quadrant III, and sine is negative there.
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Trigonometric Functions Practice Problems

These problems follow the trigonometric functions lesson. Angles are in radians.

The definitions

Common mistakes to watch for

  • Mixing up the ratios. SOH CAH TOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.
  • Calculator in the wrong mode. is in degrees but about in radians. Check the mode before every problem.
  • Wrong sign in other quadrants. Sine is positive in quadrants I and II, cosine in I and IV, tangent in I and III.
  • Forgetting tangent can be undefined. , so it does not exist where , such as at .

Frequently Asked Questions

How do I type square roots?+

Use sqrt( ), for example sqrt(3)/2 or -sqrt(2)/2. A decimal accurate to three places is also accepted.

How do I find the sign of a trig function?+

Use the quadrant: all are positive in I, sine in II, tangent in III and cosine in IV.

Calculators for this topic

Right Triangle Calculator

More practice problems

Radians and Degrees Practice Problems Inverse Functions Practice Problems Function Notation Practice Problems