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Finding the trigonometric functional values of angles that are not related to the special angles usually requires the use of a calculator.
Example - Problem 2: Two lines tangent to a circle at points M and N have a point of intersection A. A line through the center C of the circle and a point of tangency to the circle is perpendicular to the tangent line, hence the right angles at M and N in the figure below. Trigonometric ratio is a ratio that describes a relationship between a side and angle of a triangle. The inverse trigonometric functions are the inverse functions of the trigonometric functions.
In trigonometry, two angles are said to be allied when their sum or difference is a multiple of 90.
The mean proportion is any value that can be expressed just the way that 'x' is in the proportion on the left. It turns out the when you drop an altitude (h in the picture below) from the the right angle of a right triangle, the length of the altitude becomes a geometric mean. To better understand how the altitude of a right triangle acts as a mean proportion in similar triangles, look at the triangle below with sides a, b and c and altitude H.

Below is a picture of the many similar triangles created when you drop the altitude from a right angle of a right triangle. Students usually have to solve 2 different core types of problems involving the geometric mean. As you can see in the picture below, this problem type involves the altitude and 2 sides of the inner triangles ( these are just the two parts of the large outer triangle's hypotenuse) .
Involves the hypotenuse of the large outer triangle, one its legs and a side from one of the inner triangles.
This problem is just example problem 2 because it involves the outer triangle's hypotenuse, leg and the side of an inner triangle. The size of angle MAN is equal to x degrees and the length of the radius of the circle is equal to r. The six trigonometric ratios (sin x, cos x, tan x, csc x, sec x, cot x) relate the sides of a right triangle to its angles. The trigonometric ratios are functions whose input is an angle and whose output is a ratio of two lengths of the right angle triangle. For instance, the Ancient Greeks were able to use trigonometry to calculate the distance from the Earth to the Moon.Later trigonometry was developed to be the branch of mathematics that studies about relationships between angles and sides of right triangles.

This branch of mathematics defines six important trigonometric ratios which are as follows sine, cosine, tangent, cosecant, secant, cotangent. In a right triangle, the side opposite to the right angle is known as the hypotenuse, the side that is perpendicular is termed as adjacent and third side is known as base.
Trigonometric ratios are called so because all of these are defined as specified relationships between ratios of sides and angles of the right-angled triangles.
The ratios sine, cosine and tangent are main ratios; while cosecant, secant and cotangent are the inverse function of sine, cosine, tangent respectively. Let us go ahead in this page and understand more about trigonometric ratios, their definitions, important formulae and sample problems based on those.

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