Trigonometric Ratios Of Some Specific Angles

Trigonometric Ratios Of Some Specific Angles

TRIGONOMETRIC RATIOS OF 45º:

Let ΔABC be a right-angled triangle in which ∠B = 90º and ∠A = 45º.

Then, ∠C = 45º [Angle sum property]

∠A = ∠C ⇒ AB = BC. [Side opposite to equal angles]

TRIGONOMETRIC RATIOS OF 60º AND 30º:

T-RATIOS OF 60º:

In right-angled ΔADB, we have

base = BD = x; perpendicular = AD = √3x and hypotenuse = AB = 2x

T-RATIOS OF 30º:

In right-angled ΔADB, we have

base = AD = √3x, perpendicular = BD = x and hypotenuse = AB = 2x.

TRIGONOMETRIC RATIOS OF 0º:

In the figure (i), ΔABC is right angled at B and ∠BAC = θ.

In figure (ii), ∠BAC is reduced and it is less than θ. Here, we observe that the point C moves closer to the point B.

In figure (iii), ∠BAC is very small and the point C is also very close to the point B.

In figure (iv), ∠BAC just reduces to 0º and the point C coincides with the point B, i.e.,
BC = 0 and AB = AC. Then by definition, the values of the trigonometric ratios of 0º are as under:

Hence, we have

sin 0º = 0, cos 0º = 1, tan 0º = 0, sec 0º = 1.

The values of cosec 0º and cot 0º are not defined as real numbers.

TRIGONOMETRIC RATIOS OF 90º:

.

Hence, we have the values of the trigonometric ratios of 90º as under:

sin 90º = 1, cos 90º = 0, cosec 90º = 1, cot 90º = 0.

The values of sec 90º and tan 90º are not defined as real numbers.