T-Ratio of Allied Angles

What is meant by allied angles?

Allied angles are a pair of angles whose sum or difference is a multiple of 90 degrees. For example, 150° and 30° form a pair of allied angles.

What are practical examples of allied angles?

Allied angles are very common in geometry. Their examples include complementary angles (angles that sum up to 90°), supplementary angles (angles that sum up to 180°), linear pair angles (angles formed on a line), co-interior angles (angles that lie on the same side of a transversal), etc.

How is the T-ratio of allied angles related?

Using the properties of allied angles, one can break a larger angle to a smaller angle, and determine value of the T-ratio for the larger angle. For example, sin (90°+θ) can be written as -cos θ and in this way we were able to break the (90°+θ) to θ, for which the value of T-ratio is known.

What are practical applications of allied angles?

Allied angles have applications in various fields such as wave motion, harmonic motion (as they involve periodicity), signal processing, structural analysis, and navigation, etc.

Can allied angles be negative?

Yes, allied angles can be negative. Only condition that is required to be met is that their sum or difference must be a multiple of 90 degrees.

Allied Angles are a pair of angles whose sum or difference is a multiple of 90 degrees or π/2 radians. For instance, 120° and 60° are allied angles as they sum up to 180°, a multiple of 90°.

Cartesian Plane is divided into four quadrants each comprising 90°. Different trigonometric ratios have distinct properties in these quadrants such as all T-ratios being positive in the 1st quadrant which ranges from 0° to 90° and only sine and cosecant being positive in the 2nd quadrant. Thus, when one angle transitions from one quadrant to another, the trigonometric ratio changes its sign or its complementary, e.g. sine to cosine and vice versa.

In this article, we will discuss the allied angles, formulae of T-ratios of allied angles, examples of allied angles, problems on allied angles, and related frequently asked questions.