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5.5 Solving Right Triangles

5.5 Solving Right Triangles. How do we find missing angle measurements? How do we evaluate inverse trig functions?. If I told you what could be? If I told you what could be? If I told you what could be? We can do this without the table too.

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5.5 Solving Right Triangles

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  1. 5.5 Solving Right Triangles How do we find missing angle measurements? How do we evaluate inverse trig functions?

  2. If I told you what could be? If I told you what could be? If I told you what could be? We can do this without the table too. Sketch the triangle for each and “guess” the angle. • Which special (reference) angle is that? • Where else can those numbers be found?

  3. We can do this without the table too Sketch the triangle for each and “guess” the angle. Knowing “All Students Take Calculus” where else can we find that angle and ratio? • Which special (reference) angle is that? • Where else can those numbers be found? • Which special (reference) angle is that? • Where else can those numbers be found? • Which special (reference) angle is that? • Where else can those numbers be found?

  4. Inverses – “undo” • Multiplication and Division • Addition and subtraction • Square and Square root • Sine and arcsine • vs – what number times itself will give you 9? • - what angle will give you a sine ratio of ? • Notation: • Or

  5. Example 1: write each equation using proper inverse notation, then Determine all the angles which make the equation true.

  6. Example 3: Suppose is an angle in standard position whose terminal side lies in the given quadrant. Use the given trig value to find the other 5 trig functions. 1. Place triangle and find the third side using the Pythagorean theorem. 2. Use the quadrant to double check the signs (+/-) 3. Use O/y, A/x, H/r to write the rest of the trig ratios • A. Q II RECALL H 25 O 24 -7 A

  7. Example 2: Evaluate each expression (assume all angles are in QI) • Sketch the triangle using the given inverse. • Use the Pythagorean theorem to find the missing side (if needed). • Write the ratio.

  8. Example 2: Evaluate each expression (assume all angles are in QI) • Sketch the triangle using the given inverse. • Use the Pythagorean theorem to find the missing side (if needed). • Write the ratio. • Did we need to find all three sides? Why not?

  9. Example 2: Evaluate each expression (assume all angles are in QI) • Sketch the triangle using the given inverse. • Use the Pythagorean theorem to find the missing side (if needed). • Write the ratio.

  10. Summary • 1. Find all x such that , . • 2. Evaluate . Assume all angles are in quadrant I. • 3. Give the smallest positive degree value for the solution to . • 4. Which of the following trig values is equal to ?

  11. Summary • Find all x such that , . • 2. Evaluate . Assume all angles are in quadrant I. • 3. Give the smallest positive degree value for the solution to . • 4. Which of the following trig values is equal to ?

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