Let’s discuss each topic of Introduction to Trigonometry one-by-one

Trigonometric Ratios

Trigonometric Ratios are defined for the ratio of sides of any right triangle. We know that, a right triangle has 3 sides. We can obtain 6 different ratios using these side and each of these ratios has a specific name, for example,

Values of Trigonometric Ratios for angles 0°,30°,45°,60° and 90°

The standard angles for which we study values of trigonometric ratios are 0°,30°,45°,60° and 90°. These values will help you solve questions from this chapter as well as the next chapter that is applications of trigonometry.

Note that:

• The values for sec 90°, cosec 0°, tan 90° and cot 0° are not defined.
• The value of sin? or cos? never exceeds 1, whereas the value of sec? or cosec? is always greater than or equal to 1.
• These values can be derived geometrically and its derivation can be asked in boards.

Trigonometric Ratios of Complementary Angles:

Two angles are said to be complementary if their sum is equal to 90°. The relationship between the value of trigonometric ratios of complementary angles is as follows:
sin (90° – ?) = cos ?
cos (90° – ?) = sin ?
tan (90° – ?) = cot ?
cot (90° – ?) = tan ?
sec (90° – ?) = cosec ?
cosec (90° – ?) = sec ?

Note: This is defined for all values of ? when 0°<?<90°. But when ? = 0° or 90°, we need to check if the values are defined for a particular ratio or not. For example: tan90° is not defined.

Trigonometric Identities

There are 3 basic trigonometric identities which can be listed as:

• sin2?+cos2?=1, for all values of ?
• sec2?−tan2?=1, for 0°≤?<90°
• cosec2?=1+cot2?, for 0°<?≤90°

Lets solve a question based on these concepts:

Q. Evaluate

Let’s solve one of the questions: