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Navigation Review

Navigation Review. A passenger in an airplane flying at an altitude of 10km sees 2 towns directly to the east of the plane. The angles of depression to the towns are 28 o and 55 o . How far apart are the towns? 11.81 miles. One More.

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Navigation Review

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  1. Navigation Review • A passenger in an airplane flying at an altitude of 10km sees 2 towns directly to the east of the plane. The angles of depression to the towns are 28o and 55o. How far apart are the towns? • 11.81 miles

  2. One More • A plane is 160 miles north and 85 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? • N 27.98o E

  3. Basic Trigonometric Identities2.4 JMerrill, 2006 Revised, 2009 (contributions from DDillon)

  4. Trig Identities • Identity: an equation that is true for all values of the variable for which the expressions are defined

  5. Recall

  6. Recall -2 3

  7. Fundamental Trigonometric Identities Reciprocal Identities Also true:

  8. Using the Reciprocal Identities • If sin θ = x, find csc θ. • If find sin θ

  9. Fundamental Trigonometric Identities Quotient Identities

  10. Using the Quotient Identities • If Is there an easier way to find cotθ?

  11. Notation • We will now begin looking at squared trig functions. • (sinθ)2 is written sin2θ. We write the square over the word because we are not squaring the angle (sinθ2), we are squaring the sine of the angle.

  12. Fundamental Trigonometric Identities These are crucial! You MUST memorize them. You will not be able to do any of our future work if you do not know them! Pythagorean Identities

  13. Pythagorean Memory Trick sin2 cos2 tan2cot2 sec2 csc2 (Add the top of the triangle to = the bottom) 1

  14. Different Forms Pythagorean Identities appear in other forms

  15. Example • Find cosθ and tanθ if sinθ = and θ is in QII. • First we will use Identities:

  16. Example

  17. Example • Same problem—using triangles: • Find cosθ and tanθ if sinθ = and θ is in QII. 5 4 -3

  18. Simplifying #1

  19. Simplifying #2

  20. Simplifying - You Do • Simplify tanx cscx sec x

  21. One More Thing • The test is next Tuesday. • Work through the Chapter Reviews and Practice Tests • Know the Identities • Know your trig functions in terms of x,y,r • Know the exact value from the chart on P39 (sin, cos, tan) • Email me with any questions over the weekend. I’ll check email! • I’ll put power points and lab on my website on Saturday. • The lab is due next Thursday—not Tuesday.

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