We will learn about the trigonometric ratios of angle \(\frac{A}{3}\) in terms of angle A.
How to express sin A, cos A and tan A in terms of \(\frac{A}{3}\)?
(i) For all values of the angle A we know that, sin 3A = 3 sin A - 4 sin\(^{3}\) A
Now replacing A by \(\frac{A}{3}\) in the above relation then we obtain the relation as,
sin A = 3 sin \(\frac{A}{3}\) - 4 sin\(^{3}\) \(\frac{A}{3}\)
(ii) For all values of the angle A we know that, cos 3A= 4 cos\(^{3}\) A - 3 cos A
Now replacing A by \(\frac{A}{3}\) in the above relation then we obtain the relation as,
cos A = 4 cos\(^{3}\) \(\frac{A}{3}\) - 3 cos \(\frac{A}{3}\)
(iii) For all values of the angle A we know that, tan 3A = \(\frac{3 tan A - tan^{3} A}{1 - 3 tan^{2} A}\)
Now replacing A by \(\frac{A}{3}\) in the above relation then we obtain the relation as,
tan A = \(\frac{3 tan \frac{A}{3} - tan^{3} \frac{A}{3}}{1 - 3 tan^{2} \frac{A}{3}}\)
11 and 12 Grade Math
From Trigonometric Ratios of Angle A/3 to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 08, 24 10:53 AM
Oct 07, 24 04:07 PM
Oct 07, 24 03:29 PM
Oct 07, 24 03:13 PM
Oct 07, 24 12:01 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.