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Problem Solving in Trigonometry: Angles, Boats, and Complex Numbers

In this activity, we tackle a series of mathematical problems involving trigonometry and complex numbers. First, we find the distance between two boats traveling at different speeds and an angle of 54° after 3 hours. Next, we express complex numbers in trigonometric form and standard form, convert angles to decimal notation, and find exact values involving sine and cosine functions. We also simplify products involving trigonometric identities and determine sine and secant values in specified quadrants. This exercise sharpens problem-solving skills using trigonometry concepts.

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Problem Solving in Trigonometry: Angles, Boats, and Complex Numbers

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Presentation Transcript

  1. Math 1112 Activity Week #13

  2. 1. Solve the problem • Two boats leave a dock together. Each travels in a straight line. The angle between their courses measures 54°. One boat travels 36.2 kilometers per hour and the other 45.6 kilometers per hour. How far apart will they be after 3 hours?

  3. 2. Write in trig form: • A. -1 + i (Use degrees) • B. 4i (Use radians)

  4. 3. Write in standard a + bi form: • A. 5(cos 150° + isin 150°) • B. 3(cos 2π + isin 2π)

  5. 4. Convert to decimal degree notation: • 53° 44ˊˊ

  6. 5. Find the exact value:

  7. 6. Multiply & Simplify: • (1 – cos x)(1 + cos x)

  8. 7. Find exact value: • sin 185°cos65° - cos185°sin65°

  9. 8. Find sec θ • Given: and the terminal side is in quadrant II

  10. 9. Find sin2θ • Given: with θ in quadrant III

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