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Trigonometry

Trigonometry. Review. Instant Trig. Trigonometry is math, so many people find it scary However, 95% of all the “ trig ” you ’ ll ever need to know can be covered in 15 minutes. 20°. 44°. 30°. 120°. 68°. 68°. 20°. 44°. 30°. 68°. + 130°. + 68°. 180°. 180°. Angles add to 180°.

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Trigonometry

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  1. Trigonometry Review

  2. Instant Trig • Trigonometry is math, so many people find it scary • However, 95% of all the “trig” you’ll ever need to know can be covered in 15 minutes

  3. 20° 44° 30° 120° 68° 68° 20° 44° 30° 68° + 130° + 68° 180° 180° Angles add to 180° • The angles of a triangle always add up to 180°

  4. We only care about right triangles A right triangle is one in which one of the angles is 90° Here’s a right triangle: Here’s the angle we are looking at Right triangles Here’s the right angle hypotenuse opposite adjacent

  5. We call the longest side the hypotenuse We pick (or told to use) one of the other angles--not the right angle We name the other two sides relative to that angle Here’s the angle we are looking at Right triangles Here’s the right angle hypotenuse opposite adjacent

  6. If you square the length of the two shorter sides and add them, you get the square of the length of the hypotenuse adj2 + opp2 = hyp2 32 + 42 = 52, or 9 + 16 = 25 The Pythagorean Theorem

  7. There are few triangles with integer sides that satisfy the Pythagorean formula 3-4-5 and itsmultiples (6-8-10, etc.)are the best known 5-12-13 and its multiples form another set 25 + 144 = 169 hyp opp adj 5-12-13

  8. Each of these six ratios has a name (and an abbreviation) Three ratios are most used: sine = sin = opp / hyp cosine = cos = adj / hyp tangent = tan = opp / adj The ratios depend on the shape of the triangle (the angles) but not on the size hypotenuse hypotenuse opposite opposite adjacent adjacent Ratios

  9. With these functions, if you know an angle (in addition to the right angle) and the length of a side, you can compute all other angles and lengths of sides hypotenuse opposite adjacent Using the ratios • To calculate a side ratio take the tan/sin/cos of the angle Tan θ = opp/adj • To calculate an angle take the tan-1/sin-1/cos-1 of the side ratio θ = tan-1 (opp/adj)

  10. If you know the angle marked in red and you know the length of the adjacent side, then tan A = opp / adj, so length of opposite side is given byopp = adj * tan A cosA = adj / hyp, so length of hypotenuse is given byhyp = adj / cosA hypotenuse opposite adjacent Using the ratios

  11. hypotenuse opposite adjacent The Hard Part • Here’s the part I’ve always found the hardest: • Which ratio do you use and when? • It depends on what you are given! • If given opp + adj use tan • If given opp + hyp use sin • If given adj + hyp use cos • sin A = opp / hyp • cos A = adj / hyp • tan A = opp / adj

  12. Mnemonics from wikiquote • The formulas for right-triangle trigonometric functions are: • Sine = Opposite / Hypotenuse • Cosine = Adjacent / Hypotenuse • Tangent = Opposite / Adjacent • Mnemonic for those formulas are: • Some Old Horse Caught Another Horse Taking Oats Away • Saints On High Can Always Have Tea Or Alcohol • SOHCAHTOA

  13. Solve for angle A and C

  14. Solve for A and B

  15. Find x in mm’s

  16. Find x in m’s

  17. Solve each Triangle

  18. Solve each Triangle

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