Answer to Question #137067 in Trigonometry for jay nerves

Question

How do you draw/interpret the Napier’s circle?
What do you mean by Napier’s Formula?
How do you formulate Napier’s Formula?
How do you derive formula from the formulated Napier’s Formula

Answer 1

How do you draw/interpret the Napier’s circle?

It is a way used to solve spherical trigonometry, whereby 10 equations in spherical trigonometry are reduced to 2 equations, hence it can be mastered easily and more so remembered.

 

 

What do you mean by Napier’s Formula?

 The sine of any part is equivalent to the result of the digressions of the neighboring parts and the sine of any part is equivalent to the result of the cosines of the contrary parts.

 

 

How do you formulate Napier’s Formula?

Draw a right triangle on a sphere and label the sides p, q, and r where r is the hypotenuse. Let P be the angle opposite side p, Q the angle opposite side q, and R the right angle opposite the hypotenuse r.

 

How do you derive formula from the formulated Napier’s?

There are 10 equations relating the sides and angles of the triangle:

 

sin a = sin A sin c = tan b cot B

sin b = sin B sin c = tan a cot A

cos A = cos a sin B = tan b cot c

cos B = cos b sin A = tan a cot c

cos c = cot A cot B = cos a cos b

The edges they subtend at the focal point of the circle. For a circle of unit range, these edges (in radians) Each circular triangle has three edges and three sides. The sides are likewise communicated as points, equivalent the lengths of the sides. Napier's Rules apply to right-calculated triangles. Overlooking the correct point, we compose the staying five edges all together on a pie outline.

On the off chance that we select any three edges, we will consistently have a center one and either two edges adjoining it or two edges inverse to it. At that point Napier's Rules are:

Sine of middles point = Product of tangents of Adjacent edges

Sine of middles point = Product of cosines of Opposite edges