conditional trigonometric identities

In the above topics many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship exists among the angles considered. Many int..

The trigonometric ratio's are: Sine, Cosine, Tangent, Cotangent, Secant, and Cosecan..

Some Trigonometrical Identities - 1. sin A = cos (90 o - A) 2. 3. tan A x tan (90 o - A) = 1 4. sin 2 A + cos 2 A = 1 5. 1 + tan 2 A = sec 2 A 6. 1 + cot 2 A = cosec 2 A Let us prove the above identities. Let D ABC be a right-angled triangle with B = 90 o . Let BC = a,..

1. sin A = cos (90 o - A). 2. sin A / cos a = tan A. 3. tan A x tan (90 o - A) = 1. 4. sin 2 A + cos 2 A = 1. 5. 1 + tan 2 A = sec 2 A. 6. 1 + cot 2 A = cosec 2 A. Where 'A' is the angl..

Introduction - Let us recapitulate the trigonometric ratios (t-ratios). There are six t-ratios. D ABC is a right-angled triangle, B = 90 o . (i) In short, (ii) In shor..

\ The Circular function of a real number q and the trigonometric function for the angle q c are same. The identities for circular functions of real numbers hold for trigonometric functions of angle q..

Logical Equivalence - Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth..

Degree/radian measures Basic trigonometric functions Special right triangles Trigonometric values of standard angles Justify the Pythagorean identities Trigonometric equations (0 to 360 degrees..

Variation may be defined as differences among individuals of a species. All around us we see different organisms belonging to different species. Within each species too, no two individuals are identical to each other. Asexual reproduction produces identical offspring called clon..

Crystals are solid particles bounded by plane surfaces, which make definite angles with each other. This gives a definite geometrical shape to the crystal. These shapes are different for different crystals (Fig.6.13). Crystals of the same substance are identical only under iden..