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Module 13 Review 2/7/2019

Learn how to simplify expressions, calculate tangent, sine, and cosine ratios, solve for missing lengths and angles, and identify special right triangles. Prepare for the Module 13 Quiz.

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Module 13 Review 2/7/2019

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  1. Module 13 Review2/7/2019 9-22-2014

  2. Warmups Simplify the following expressions, this DOES NOT mean a decimal approximation. 2. + 4 +3 3. 2 (3) 4.

  3. The Tangent Ratio These slides are your official notes for the Module 13 Quiz on Friday, 2/8. The tangent of θ is defined as the opposite side divided by the adjacent side. Mathematically, this is written as: • tanθ =

  4. The Tangent Ratio Find the tangent ratio (simplified fraction) for each of the acute angles in the figures below.

  5. The Tangent Ratio Use the tangent ratio to solve for missing length.

  6. The Tangent Ratio We can use the “inverse tangent” to find missing angle measures. Remember to use the “2nd” button.

  7. Sine and Cosine Ratios The sine of θ is defined as the opposite side divided by the hypotenuse. Mathematically, this is written as: • sinθ = The cosine of θ is defined as the adjacent side divided by the hypotenuse. Mathematically, this is written as: • cosθ =

  8. Sine and Cosine Ratios You can use these definitions to calculate trigonometric ratios other than the tangent. • Write each trigonometric ratio as a fraction (these are NOT “button problems”):

  9. Sine and Cosine Ratios Now find missing side lengths, x, using sine or cosine in the figures below (these ARE “button problems”).

  10. Sine and Cosine Ratios We can use the “inverse sine” and “inverse cosine” to find missing angle measures. Remember to use the 2nd button. Find the measure of each given angle. Find m∠U Find m∠P

  11. Special Right Triangles What are the Special Right Triangles? 30-60-90 45-45-90

  12. Special Right Triangles Find the unknown side lengths in the right triangles below.

  13. Special Right Triangles Pythagorean Triples are a set of positive integers that satisfy the Pythagorean Theorem a2 +b2 = c2. Verify that the side lengths below are Pythagorean triples: 3, 4, and 5 Yes, 25 = 25 8, 15, and 19 No, 289 ≠ 361 7, 24, and 25 Yes, 625 = 625

  14. Assignment Remember, the Module 13 Review Packet is due tomorrow.

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