Mathematics 1 Past Paper NUST Fall 2024 PDF

National University of Sciences and Technology (NUST) H-12, Islamabad, Pakistan Mathematics – 1 Fall Semester-2024 Dr. Hassan Anwer Department of Environmental Engineering Email: [email protected] Research profile: https://www.researchgate.net/profile/Hassan-Anwer CHAPTER 5 Radians and D...

National University of Sciences and Technology (NUST) H-12, Islamabad, Pakistan Mathematics – 1 Fall Semester-2024 Dr. Hassan Anwer Department of Environmental Engineering Email: [email protected] Research profile: https://www.researchgate.net/profile/Hassan-Anwer CHAPTER 5 Radians and Degrees Circle Arc and Area Measure Applications of Circle Arc and Area Trigonometric Functions Applications of Trigonometric Functions Application Designing a photocatalytic reactor A company manufactures TL-60 lamps for photocatalytic reactors. The lamps light arc subtends an angle of π/6 radians at the face of the lamp. An environmental engineer wants to install TL-60 lamps in a cylindrical photocatalytic reactor having a diameter of 4 m. How many lamps will be needed for complete illumination of the reactor? Application Designing a photocatalytic reactor Radius = 2 m Angle subtended by arc = π/6 rad Arc length = s = rθ = 2 m x π/6 = π/3 m Circumference of reactor = 2πr = 2π (2 m) = 4π m Total lamps needed = Circumference/Arc length=(4π m)/(π/3 m) = 12 12 lamps will be needed for reactor illumination Find area of a single pizza slice if the diameter is 16 inches TRIGNOMETRIC FUNCTIONS PYTHAGORUS THEOREM FORMULA TRIGNOMETRIC FUNCTIONS The Height of a Structure Distance Across An Obstruction An environmental engineer is tasked with measuring the width of a river but cannot cross it. She sets up her equipment on one bank of the river and identifies a tree directly across on the other bank. From her position, she walks 150 ft downstream, keeping her sight on the tree, and measures the angle between her line of sight to the tree and the perpendicular line across the river as θ=45°. Determine the width of the river using trigonometry. Distance Across An Obstruction Integrating Circle and Triangle Formulas A solid sphere with a diameter of 1.5 feet needs to be moved to a rooftop 12 feet high using an inclined plane. The plane is inclined at an angle of 35° with the ground. Calculate the number of revolutions the sphere must make to reach the rooftop. 12 ft 35° Integrating Circle and Triangle Formulas An arc of a circle is inscribed in a right triangle with a perpendicular of 9 feet and an opposite angle of 45°. If the radius of the arc is equal to the base of the triangle, calculate the length of the arc. 9 ft 45° THANK YOU