Grade 10 Mathematics Trigonometry Mathematics Proper Thinking Accuracy

Grade 10 Mathematics Trigonometry ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The sine of any angle If the point P is taken to revolve about a unit circle then sin θ is given by the y-coordinate of the point P. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The cosine of any angle If the point P is taken to revolve about a unit circle then cos θ is given by the x-coordinate of the point P. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The tangent of any angle Tan θ is given by the y-coordinate of the point P divided by the x-coordinate. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The tangent of any angle Tan θ can also be given by the length of the tangent from the point P to the x-axis. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 Remember CAST We can use CAST to remember in which quadrant each of the three ratios is positive. 2 nd quadrant 1 st quadrant S Sine is positive A All are positive 3 rd quadrant 4 th quadrant T Tangent is positive C Cosine is positive ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = sin θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of sin θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = sin θ The graph of sine is said to be periodic since it repeats itself every 360°. We can say that the period of the graph y = sin θ is 360°. Other important features of the graph y = sin θ include the fact that: It passes through the origin, since sin 0° = 0. The maximum value is 1 and the minimum value is – 1. Therefore, the amplitude of y = sin θ is 1. It has rotational symmetry about the origin. In other words, it is an odd function and so sin (–θ) = –sin θ. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = cos θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of cos θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = cos θ Like the graph of y = sin θ the graph of y = cos θ is periodic since it repeats itself every 360°. We can say that the period of the graph y = cos θ is 360°. Other important features of the graph y = cos θ include the fact that: It passes through the point (0, 1), since cos 0° = 1. The maximum value is 1 and the minimum value is – 1. Therefore, the amplitude of y = cos θ is 1. It is symmetrical about the y-axis. In other words, it is an even function and so cos (–θ) = cos θ. It is the same as the graph of y = sin θ translated left 90°. In other words, cos θ = sin (90° – θ). ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = tan θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of tan θ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 The graph of y = tan θ You have seen that the graph of y = tan θ has a different shape to the graphs of y = sin θ and y = cos θ. Important features of the graph y = tan θ include the fact that: It is periodic with a period of 180°. It passes through the point (0, 0), since tan 0° = 0. Its amplitude is not defined, since it ranges from +∞ to –∞. It is symmetrical about the origin. In other words, it is an odd function and so tan (–θ) = –tan θ is not defined for θ = ± 90°, ± 270°, ± 450°, … that is, for odd multiples of 90°. The graph y = tan θ therefore contains asymptotes at these points. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation

ML 1 A. PA 7. 7 Transforming trigonometric graphs ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation