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Lesson 1: Trigonometric Functions of Acute Angles

Lesson 1: Trigonometric Functions of Acute Angles. Done by: Justin Lo Lee Bing Qian Danyon Low Tan Jing Ling. Trigonometric Functions. The three main functions in trigonometry are  Sine ,  Cosine  and  Tangent . They are often shortened to  sin ,  cos  and  tan.

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Lesson 1: Trigonometric Functions of Acute Angles

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  1. Lesson 1:Trigonometric Functions of Acute Angles Done by: Justin Lo Lee Bing Qian Danyon Low Tan Jing Ling

  2. Trigonometric Functions • The three main functions in trigonometry are Sine, Cosine and Tangent. • They are often shortened to sin, cos and tan.

  3. Use the calculator to find the following Using your calculator… http://www.shopperhive.co.uk/compare/casio-fx83gt-calculator-prices

  4. Sin, Cos, Tan A Hypotenuse Let this angle be x Opposite C B Adjacent

  5. A Hypotenuse Let this angle be x Opposite SOH CAH TOA • "Opposite" is opposite to the angle x • "Adjacent" is adjacent (next to) to the angle x • "Hypotenuse" is the longest line C B Adjacent

  6. Example 1: Find sin Line B (Hypotenuse) = 2 cm Line C = 1 cm Line C is opposite to angle Solution: Recall the formula: S Line A = cm Length of Line C (Opposite) Length of Line B (Hypotenuse)

  7. Example 2: Find Line B (Hypotenuse) = 2 cm Line C = 1 cm Line C is adjacent to angle Solution: Recall the formula: Line A = cm Length of Line C (Adjacent) Length of Line B (Hypotenuse)

  8. Example 3: Line B (Hypotenuse) = cm Find Line C = 1 cm Solution: Line A = 1 cm Recall the formula: Length of Line A/C (Opposite) Length of Line C/A (Adjacent)

  9. A B C

  10. Note: • Always draw a diagram to visualise if confused! • What if the triangle is not right-angled? Can we still use sin, cos, tan? • Angle of reference • Applies to adjacent and opposite too • Dependent on angle not triangle

  11. Think… • How far up a wall could Bob the Builder reach with a 30 foot ladder, if the ladder makes a 70° angle with the ground? (2d.p) 0.93969= y= 28.19 30 y

  12. Refer to Worksheet

  13. Inverse Trigonometric Functions • Just as the square root function  is defined such that y2 = x, the function y = arcsin(x) is defined so that sin(y) = x

  14. False!

  15. Example 4: Find 5 cm x 3 cm Solution: Answer Recall the formula: 4cm

  16. Example 5: Find 13 cm x 5 cm Solution: Answer Recall the formula: 12cm

  17. Example 6: Find 13 cm x 5 cm Solution: Answer Recall the formula: tan 12cm

  18. WORKSHEET TIME!

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