Ramanujan
Henry Frederick Baker has written: 'Abel's theorem and the allied theory' -- subject(s): Abelian Functions, Functions, Abelian, Functions, Theta, Riemann surfaces, Theta Functions
Theta is a function of set as
Jun-ichi Igusa has written: 'Theta functions' -- subject(s): Abelian varieties, Commutative rings, Theta Functions
By converting cosecants and secants to the equivalent sine and cosine functions. For example, csc theta is the same as 1 / sin thetha.
R. P. Agarwal has written: 'Resonance of Ramanujan's mathematics' -- subject(s): Continued fractions, Functions, Theta, Hypergeometric series, Influence, Theta Functions
You can use your trigonometric functions (sine, cosine, and tangent).
They are mathematical functions. Most people are introduced to them as trigonometric functions. In the context of a right angled triangle, with one of its angles being theta, Cos(theta) = The ratio of the lengths of the adjacent side and the hypotenuse. Sin(theta) = The ratio of the lengths of the opposite side and the hypotenuse. More advanced mathematicians will know them simply as the following infinite series: Cos(theta) = 1 - x2/2! + x4/4! - x6/6! + ... and Sin(theta) = x/1! - x3/3! + x5/5! - x7/7! + ... n! = 1*2*3* ... *n
sin theta and csc theta are reciprocal functions because sin = y/r and csc = r/y you use the same 2 sides of a triangle, but you use the reciprocal.
The complex number exp(i theta) is significant in trigonometry and exponential functions because it represents a point on the unit circle in the complex plane. This number can be used to express trigonometric functions and rotations in a concise and elegant way, making it a powerful tool in mathematical analysis and problem-solving.
Sine Theta (sin θ) = opposite/hypotenuse = a/c Cosine Theta (cos θ) = adjacent/hypotenuse = b/c Tangent Theta (tan θ) = opposite/adjacent = a/b Cotangent Theta (cot θ) = adjacent/opposite = b/a Secant Theta (sec θ) = hypotenuse/adjacent = c/b Cosecant Theta (csc θ) = hypotenuse/opposite = c/a You may need to look on the link below for some sample calculations
The only real solution is theta = 0For theta < 0 square root of 3 theta is not defined.For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.The only real solution is theta = 0For theta < 0 square root of 3 theta is not defined.For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.The only real solution is theta = 0For theta < 0 square root of 3 theta is not defined.For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.The only real solution is theta = 0For theta < 0 square root of 3 theta is not defined.For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.
tan2(theta) + 5*tan(theta) = 0 => tan(theta)*[tan(theta) + 5] = 0=> tan(theta) = 0 or tan(theta) = -5If tan(theta) = 0 then tan(theta) + cot(theta) is not defined.If tan(theta) = -5 then tan(theta) + cot(theta) = -5 - 1/5 = -5.2