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The Trigonometric Functions we will be looking at

The Trigonometric Functions we will be looking at. SINE. COSINE. TANGENT. The Trigonometric Functions. SIN E. COS INE. TAN GENT. SIN E. Pronounced “sign”. COS INE. Pronounced “co-sign”. TAN GENT. Pronounced “tan-gent”. Greek Letter q. Pronounced “theta”.

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The Trigonometric Functions we will be looking at

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  1. The Trigonometric Functions we will be looking at SINE COSINE TANGENT

  2. The Trigonometric Functions SINE COSINE TANGENT

  3. SINE Pronounced “sign”

  4. COSINE Pronounced “co-sign”

  5. TANGENT Pronounced “tan-gent”

  6. Greek Letter q Pronounced “theta” Represents an unknown angle

  7. hypotenuse hypotenuse opposite opposite adjacent adjacent

  8. Finding sin, cos, and tan.Just writing a ratio.

  9. Find the sine, the cosine, and the tangent of theta. Give a fraction. 37 35 12 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

  10. Find the sine, the cosine, and the tangent of theta 24.5 8.2 23.1 Shrink yourself down and stand where the angle is. Now, figure out your ratios.

  11. Using Trig Ratios to Find a Missing SIDE

  12. Draw stick-man at the given angle. • Identify the GIVEN sides (Opposite, Adjacent, or Hypotenuse). • Figure out which trig ratio to use. • Set up the EQUATION. • Solve for the variable. To find a missing SIDE

  13. H 1. Problems match the WS. A Where does x reside? If you see it up high then we MULTIPLY!

  14. 2. H O Problems match the WS. Where does x reside? If X is down below,The X and the angle will switch… SLIDE & DIVIDE

  15. H 3. Problems match the WS. A

  16. Steps to finding the missing angle of a right triangle using trigonometric ratios: 5.92 km OPP ADJ 2.67 km HYP  Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle

  17. Steps to finding the missing angle of a right triangle using trigonometric ratios: 5.92 km OPP ADJ 2.67 km HYP  For the unknown angle choose the correct trig ratio which can be used to set up an equation Set up the equation

  18. Steps to finding the missing angle of a right triangle using trigonometric ratios: 5.92 km OPP ADJ 2.67 km HYP  Solve the equation to find the unknown using the inverse of trigonometric ratio.

  19. Find, to one decimal place, the unknown angle in the triangle. • Your turn Practice Together: 3.1 km 2.1 km 

  20. Find, to 1 decimal place, the unknown angle in the given triangle. YOU DO: 7 m 4 m 

  21. Sin-CosineCofunction

  22. The Sin-Cosine Cofunction

  23. 1. What is sin A? 2. What is Cos C?

  24. 3. What is Sin Z? 4. What is Cos X?

  25. 5. Sin 28 = ?

  26. 6. Cos 10 = ?

  27. 7. ABC where B = 90.Cos A = 3/5What is Sin C?

  28. 8. Sin  = Cos 15What is ?

  29. Trig Application Problems MM2G2c: Solve application problems using the trigonometric ratios.

  30. Depression and Elevation horizontal angle of depression line of sight angle of elevation horizontal

  31. 9. Classify each angle as angle of elevation or angle of depression. Angle of Depression Angle of Elevation Angle of Depression Angle of Elevation

  32. Example 10 • Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation to the nearest degree? 5280 feet – 1 mile

  33. Example 11 • The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder? Round to the nearest whole number.

  34. Example 12 • Find the angle of elevation to the top of a tree for an observer who is 31.4 meters from the tree if the observer’s eye is 1.8 meters above the ground and the tree is 23.2 meters tall. Round to the nearest degree.

  35. Example 13 • A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the building? Round to the nearest degree.

  36. Example 14 • A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from the boat and swims 935 feet to reach the wreck. What is the angle of depression from the boat to the shipwreck, to the nearest degree?

  37. Example 15 • A 5ft tall bird watcher is standing 50 feet from the base of a large tree. The person measures the angle of elevation to a bird on top of the tree as 71.5°. How tall is the tree? Round to the tenth.

  38. Example 16 • A block slides down a 45 slope for a total of 2.8 meters. What is the change in the height of the block? Round to the nearest tenth.

  39. Example 17 • A projectile has an initial horizontal velocity of 5 meters/second and an initial vertical velocity of 3 meters/second upward. At what angle was the projectile fired, to the nearest degree?

  40. Example 18 • A construction worker leans his ladder against a building making a 60o angle with the ground. If his ladder is 20 feet long, how far away is the base of the ladder from the building? Round to the nearest tenth.

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