ATPL Navigation Exam - Sine Rule/Cosine Rule Application

[Brand Wessels]

At ATPL level the ATPL student might bump into the odd exam question that requires the application of the Trigonometric Sine Rule and Cosine Rule for the solution. In Navigation it is often used in conjunction with the Polar Stereographic Chart (often when there are two different latitudes mentioned in the question) – in Radios for RNAV calculations.

It is not particular difficult, but as with anything else in life, currency is everything. Typically you will have to use both Sine- and Cosine Rule – the one leading to the other.

Prior knowledge required:

Solid knowledge of Polar Stereographic theory:
• Also how to sketch the chart – North Polar chart means all longitudes are drawn North inwards, towards the centre. All direction is still measured clockwise from North. Greenwich is at the bottom and the International Date Line is drawn at the top of the sketch.
• South Polar chart means all longitudes are drawn from the centre with North outwards. The Greenwich line is drawn at the top and the International Date Line at the bottom of the sketch.
• All latitudes are concentric circles
• Latitudes are still 60nm apart.

Basic Trigonometry - the sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle.
The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Geometry - opposing angles between two straight lines are equal in size

Basic mathematics skills – BODMAS, inverse operation, etc.

Good understanding of your scientific calculator.

Example Question follows below...

[jimdavis]

Good stuff Brand. Haven't used Sin Cos and Tan for a hell of a long time - In fact we used to look their values up in tables. What happens now - does your calculator give you the values?

[Brand Wessels]

Good stuff Brand. Haven't used Sin Cos and Tan for a hell of a long time - In fact we used to look their values up in tables. What happens now - does your calculator give you the values?

Morning Jim - indeed it does. Same with logs. As a result there are many more questions to be done in the same exam time. The whizzwheel and CX2/3 nav computers mostly take care of the sin- and cos rules - while solving the triangle of velocities. In 2004 my first ATPL student ever (he was 59 then and from the celestial navigation era) was still able to apply all the trigonometry and manual multiplication and division without using a scientific calculator. I was very impressed - but I had to convert him to the electronics, simply because of the speed required in the exams. Interestingly enough - my youngest (now at university) still have a substantial component of manual skills requirements (no calculator allowed). They feel it is important for the student to still understand the thinking process - correctly so.

[Brand Wessels]

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[ACE MAN]

Good stuff Brand. Haven't used Sin Cos and Tan for a hell of a long time - In fact we used to look their values up in tables. What happens now - does your calculator give you the values?

I had this dilemma doing my CPL n 1995 having only used the Trig books, now having to work out COSEC/COTAN/SEC by using the INV function on a calculator had me cross eyed - tks to a sharp kid on course with me (Mason - rip- son of a Safair FE) who sat with me for an hour over beers in a GC nightclub explaining the calculator use on this.

[Brand Wessels]

Good stuff Brand. Haven't used Sin Cos and Tan for a hell of a long time - In fact we used to look their values up in tables. What happens now - does your calculator give you the values?

I had this dilemma doing my CPL n 1995 having only used the Trig books, now having to work out COSEC/COTAN/SEC by using the INV function on a calculator had me cross eyed - tks to a sharp kid on course with me (Mason - rip- son of a Safair FE) who sat with me for an hour over beers in a GC nightclub explaining the calculator use on this.

Indeed - until 2014 the ATPL students had to use Meridinial Parts Tables in Navigation and Mercator application, at least combined with scientific calculators. That certainly took me back to the Trig books of the 1970's...