• Modelling Seasonal Temperatures With the Sine Function

    Sine functions are useful for modelling some periodic phenomena. The temperature varies with the seasons, and the variation has a period of approximately one year. The average maximum temperature (°C) for Cape Town in each month is shown in the table...

    https://astarmathsandphysics.com/ib-maths-notes/trigonometry/1126-modelling-seasonal-temperatures-with-the-sine-function.html

  • Analysis of a Plane Blown Off Course

    Suppose a plane can fly 300km/h in still air. It wishes to fly from a town A to a town B on a bearing of 030 o to a town B. The wind is blowing at 20km/h on a bearing of 300 o . If the pilot aims the plane on to fly to B, he will be blow off course by...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/5031-analysis-of-a-plane-blown-off-course.html

  • Angles in Three Dimensional Solids

    Finding the angle between vertices in a three dimensional solid can be tricky. It often helps to construct a triangle between the relevant vertices. Then it is often possible to use trigonometry. Consider the hexagonal pyramid below. The base is a...

    https://astarmathsandphysics.com/gcse-maths-notes/557-angles-in-three-dimensional-solids.html

  • Finding Sides of Right Angled Triangles

    Simple trigonometry can be used with right angled triangles to a side given a side and one of the interior angles other than the right angle, With the sides of the triangle as labelled above, we can use one of the formulae: Example: If we have and and...

    https://astarmathsandphysics.com/o-level-maths-notes/342-finding-sides-of-right-angled-triangles.html

  • Practical Vectors

    Planes rarely fly in the direction they are pointing. If the wind is blowing and the world is turning the pilot has to take account of these when he plots a course. Even with modern gps systems available, , it is beneficial to the pilot to take these...

    https://astarmathsandphysics.com/o-level-maths-notes/345-practical-vectors.html

  • The Cosine Rule

    If we have a triangle, and we need to calculate angles and/or sides, we can only use simple trigonometry and Pythagoras theorem if the triangle is right angled. If the triangle is not right angled, then we must use general formulae which apply to any...

    https://astarmathsandphysics.com/o-level-maths-notes/357-the-cosine-rule.html

  • The Sine Rule

    If we have a triangle, and we need to calculate angles and/or sides, we can only use simple trigonometry and Pythagoras theorem if the triangle is right angled. If the triangle is not right angled, then we must use general formulae which apply to any...

    https://astarmathsandphysics.com/o-level-maths-notes/361-the-sine-rule.html

  • Bearings

    Bearings involve using trigonometry, generally the cosine or sinerules: Cosine Rule: Sine Rule: For the above diagram, find a)The distance BC b)The bearing of A from B and the bearing of B from C. a)Label the triangle as above, with sides labelled by...

    https://astarmathsandphysics.com/igcse-maths-notes/449-bearings.html

  • Practical Application of Vectors

    Planes do fly straight ahead. The wind blows and the world turns and the pilot has to take account of these when he plots a course. Even with modern gps systems, , it is useful to the pilot to take account of these because of the resulting decrease in...

    https://astarmathsandphysics.com/igcse-maths-notes/494-practical-application-of-vectors.html

  • Angles of Elevation

    The angle of elevation of an object is the angle a line of sight to the object makes above the horizontal, and the angle of depression is the angle of a line of sight to the object below the horizontal. We can find angles of elevation or depression...

    https://astarmathsandphysics.com/gcse-maths-notes/558-angles-of-elevation.html

  • Bearings

    Bearings involve using trigonometry, generally the cosine or sine rules: Cosine Rule: Sine Rule: For the above diagram, find a)The distance BC b)The bearing of A from B and the bearing of B from C. a)Label the triangle as above, with sides labelled by...

    https://astarmathsandphysics.com/gcse-maths-notes/560-bearings.html

  • The Need For Complex Numbers

    The general solution of the quadratic equation is and If then and are distinct real numbers. and can be plotted on the - axis, abd the graph will pass though the points and If then and the graph just touches the – axis but does not cross it. If the m...

    https://astarmathsandphysics.com/ib-maths-notes/complex-numbers/958-the-need-for-complex-numbers.html

  • River Crossing

    Planes rarely fly in the direction they are pointing. If the wind is blowing and the world is turning the pilot has to take account of these when he plots a course. Even with modern gps systems available, , it is beneficial to the pilot to take these...

    https://astarmathsandphysics.com/ib-maths-notes/vectors-lines-and-planes/1170-river-crossing.html

  • Torque and Moments

    The motion of a rigid body is in general a combination of translation and rotation. The two tyopes of motion can be treated independently. A translation takes place when every particle in a rigid body has the same velocity while a rotation is when...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1379-torque-and-moments.html

  • The Maths of Youngs's Double Slit Experiment

    Young's double slit experiment, along with the pattern formed on a screen, is illustrated below. We can derive an expression for the distance between successive slits in two different ways. Both use the fact that for a bright fringe, constructive...

    https://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/1502-the-maths-of-youngs-s-double-slit-experiment.html

  • Circular Horizontal Motion of a Ring Threading an Inelastic String

    If a ring of mass m is threaded on a string of length tied to points A and B with B vertically below A and l > AB the ring can be made to execute circular horizontal motion. Resolving vertically for the ring gives (1) Using horizontally gives (2) gives...

    https://astarmathsandphysics.com/a-level-maths-notes/m3/3636-circular-horizontal-motion-of-a-ring-threading-an-inelastic-string.html

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