your house to a nearby store‚ you must walk 4 m east and then 20 m 30° north of east. What is your displacement? Use polygon method and parallelogram method. Check you result by sine law and cosine law. COSINE LAW SINE LAW R²= a² + b² - 2 AB cos 150° = (4m) ² + (20m) ² - 2 (4m)(20m) cos 150° = 16m² + 400m² - 2 (80m²)(-0.87)
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we study seems to have little real-life application. So how much do we use trigonometry in everyday life? The answer is a lot. One of the biggest ways worldwide is music. Sound travels in waves‚ and this pattern‚ though not as regular as a sine or cosine function‚ is still useful in developing computer music. This means that sound engineers and technologists who research
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Volume of prism = area of cross section × length a = b = c Sine rule : sin A sin B sinCross C section b of c Volume of a Sine Rule: prism = area cross section × length sin A In any triangle ABC sin B sin C Cosine rule: a2 = b2 + c2 – 2bc cos A Cross section c A c B b a l r r len Cosine Rule: a2 Area of triangle = 1
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Triangles‚ Laws of Sines and Cosines INTRODUCTION: Student will demonstrate how to apply laws of sines and cosines to oblique triangles. OBJECTIVES: After completing this unit‚ the student will be able to: 6. Use the Law of Sines and the Law of Cosines to solve oblique triangle problems. 6.1. Summarize the Law of Sines. 6.2. Find the area of an oblique triangle using the sine function. 6.3. Judge when an ambiguous case of the Law of Sines occurs. 6.4. Solve applied problems using the Law of Sines
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hyp 1 3 h r opp adj = hyp cos opp = hyp sin opp = adj tan sin adj hyp tan or C opp hyp cos adj In any triangle ABC opp adj b a A B c a sin A Sine rule: b sin B c sin C Cosine rule: a2 = b2 + c2 – 2bc cos A Area of triangle = 1 2 ab sin C cross section lengt h Volume of prism = area of cross section length Area of a trapezium = r 1 2 (a + b)h a
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Time Frame | Objectives | Topics/ Content | Concept/s | Competencies | Teaching Strategy | Values | List of Activities | Materials | Evaluation | References | First Quarter | -Define functions and give examples that depict functions-Differentiate a function and a relation-Express functional relationship in terms of symbols y=f(x)-Evaluate a function using the value of x. | Chapter 1Functions and GraphsFunctions and Function Notations | The equation y=f(x) is commonly used to denote functional relationship
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Republic of the Philippines Department of Education Region IV – A CALABARZON Division of Antipolo City SAN JOSE NATIONAL HIGH SCHOOL GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS IV (Advanced Algebra‚ Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function 1.2 Differentiate a function from a mere relation * real life relationships * set of ordered pairs * graph of a given set of ordered
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false 5. The cosine law is: cos(γ)=(a²+b²-c²)/(2ab) true false Multiple Choice‚ mark your answer(s). 1. sin(20°)=45.9/c a.) c=88.79 b.) c=134.21 c.) c=50.28 d.) c=45.9/sin(20°) 2. How do you calculate the perimiter of a triangle? a.) P=a²+b²-c² b.) A=bh/2 c.) P=a+b+c c.) A=l*w 3. What would you use to find out x? a.) the sine law b.) sine the trigonomic ratio c.) first the cosine law then the sine law d.) first
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casting out nines to check whether the product‚ quotient‚ or root is correct. Objective of the study: 1. Life History of Ghiyath Ai-Din Jamshid Mas’ud Al-Kashi 2. Contribution in Mathematics 3. Multiples Algorithm and Multiple Solutions 4. Law of Cosines 5. Fixed Point Iteration Method 6. Calculation of PI 1. Life History of Jamshid al-Kashi Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380‚ in Kashan‚ in central Iran. This region was
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Spherical trigonometry Spherical trigonometry is that branch of spherical geometry which deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy‚ geodesy and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics
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