Everything Maths Grade 10

10.Iftan =

5

12

and 0 ◦  180 ◦, determinewithout the use of a calculatorthe value of

12

cos

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1.2FSP 2.2FSQ 3.2FSR 4.2FSS 5.2FST 6.2FSV

7.2FSW 8.2FSX 9.2FSY 10.2FSZ

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5.9 Chapter summary EMA3Y

See presentation:2FT2atwww.everythingmaths.co.za

• We can define three trigonometric ratios for right-angled triangles: sine (sin), cosine (cos) and tangent
  (tan)
  These ratios can be defined as:
  
  
  • sin=hypotenuseopposite =yr
  
  
  • cos=hypotenuseadjacent =xr
  
  
  • tan=oppositeadjacent=yx
  
  
  
  


• Each of these ratios have a reciprocal: cosecant (cosec), secant (sec) and cotangent (cot).
  These ratios can be defined as:
  
  
  • cosec=hypotenuseopposite =yr
  
  
  • sec=hypotenuseadjacent =xr
  
  
  • cot=oppositeadjacent=xy
  
  
  
  


• We can use the principles of solving equations and the trigonometric ratios to help us solve simple
  trigonometric equations.


• For some special angles (0°, 30°, 45°, 60° and 90°), we can easily find the values ofsin,cosandtan
  without using a calculator.


• We can extend the definitions of the trigonometric ratios to any angle.

End of chapter Exercise 5 – 8:

1.State whether each of the following trigonometric ratios has been written correctly.

a)sin=

hypotenuse

adjacent

b)tan=

opposite

adjacent

c)sec=

hypotenuse

adjacent

2.Use your calculator to evaluate the following expressions to two decimal places:

138 5.9. Chapter summary