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5.1 Trigonometric Functions of Acute Angles Wed Dec 11

5.1 Trigonometric Functions of Acute Angles Wed Dec 11. Do Now Solve for x 1) 1^2 + x^2 = 2^2 2) x^2 + x^2 = 1. CH 10 Test Review. Retakes by Monday. Trigonometric Ratios. Given a right triangle, the lengths of the sides of the triangle are used to define the six trigonometric ratios

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5.1 Trigonometric Functions of Acute Angles Wed Dec 11

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  1. 5.1 Trigonometric Functions of Acute AnglesWed Dec 11 Do Now Solve for x 1) 1^2 + x^2 = 2^2 2) x^2 + x^2 = 1

  2. CH 10 Test Review • Retakes by Monday

  3. Trigonometric Ratios • Given a right triangle, the lengths of the sides of the triangle are used to define the six trigonometric ratios • Sine (Sin) • Cosine (Cos) • Tangent (Tan) • Cosecant (Csc) • Secant (Sec) • Cotangent (Cot)

  4. Trigonometric Functions Values of an Acute Angle • Let be an acute angle of a right triangle, then the 6 trig functions are:

  5. Reciprocal Functions • Cosecant, secant, and cotangent are reciprocals of sine, cosine, and tangent respectively

  6. Ex1 • If sinx = 12/13, find the other 5 trig function values

  7. Ex 2 • Given Tanx = 4/3, find the other 5 trig function values

  8. Ex3 • If sinx = 6/7 and x is an acute angle, find the other 5 trig function values

  9. Similar Triangles and Trig • If two triangles are similar, their trigonometric function values will be the same • Ex: 3-4-5 and 12-16-20 right triangles

  10. Closure • If cosx = 4/7, find the other 5 trig values • HW: p.444 #1-15 odds

  11. 5.1 Trigonometric Functions of Acute AnglesThurs Dec 12 • Do Now • Let cscx = 5/4 Find the other 5 trig values

  12. HW Review: p.444 #1-15 odds

  13. Trig Values of 30, 45, 60 deg • Using geometry, we can construct right triangles using 30, 45, and 60 degrees, then find the trig values

  14. 30-60-90 Right Triangle

  15. 45-45-90 Right Triangle

  16. Ex • As a hot-air balloon began to rise, the ground crew drove 1.2 mi to an observation station. The initial observation from the station estimated the angle between the ground and line of sight to the balloon to be 30 degrees. Approximately how high was the baloon at that point?

  17. Decimal-Degree and Degree-Minute-Second Form • To convert from DMS to decimal degree, • 1) Use 2nd -> Angle to write degree and minute • 2) Use Alpha -> + sign to write second • To convert from decimal degree to DMS, • Use 2nd -> Angle -> DMS

  18. Ex • Convert 72.18 degrees to DMS and back

  19. Trig Values of other Angles • To find the 6 trig values of other angles, we will use the calculator. • Be sure your calculator is in the correct mode • Angles can be expressed in degrees or radians • Round to at least 3 decimal places

  20. Finding the Angle • We use inverse trig functions (has a -1) to find the angle • Ex: Find the angle whose sine value is 0.20113

  21. Ex • A paint crew has purchased new 30ft extension ladders. They extend the ladder to 25 ft and position the base 6.5 ft away from the wall. What angle does the ladder make with the ground?

  22. Cofunction Identities • Since the 2 acute angles in a right triangle will always be complementary, the following identities are a result

  23. Ex • Given sin 18 deg = 0.3090, cos 18 deg = 0.9511, and tan 18 deg = 0.3249, find the 6 trig function values of 72 degrees

  24. Closure • Given sin 8 deg = 0.1392, cos 8 deg = 0.9903, and tan 8 deg = 0.1405, find the 6 trig function values of 82 degrees • HW: p.444 #17-101 odds

  25. 5.1 ReviewFri Dec 13 • Do Now • Evaluate in exact value • 1) csc 45 deg • 2) cos 60 deg

  26. HW Review: p.444 #17-101

  27. Closure • What are the 6 trig functions? What do they tell us? • HW: none

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