Trigonometry: Double and Half Angle Formulas
This is a free lesson from our course in Trigonometry
In this lesson you'll go through the basic concepts of double angle and the half angle formulas. Further you'll deal with problems that involve angular measures and learn it with the help of some examples, practice questions with solution and using video explanations by the instructor that brings in an element of real-class room experience.
The double and half angle formulas can be used to find the values of unknown trigonometric functions. For example, you might not know the sine of 15 degrees, but by using the half angle formula for sine, you can figure it out based on the common value of sin(30) = 1/2. They are also useful for certain integration problems where a double or half angle formula may make things much simpler to solve. The use of Double-Angle formulas help reduce the degree of difficulty. (More text below video...)
<h2>Trigonometry - Double and Half Angle Formulas</h2> <p>Double and Half Angle Formulas, degree, trigonometry help, example, formula, solution, sine, cosine, sum and difference formula, sum formula, difference formula, double angle formula, half angle formula, Pythagorean identities, sin, cos, angles sum and difference formulas, practice questions, quizzes</p> <p>sin 2A = 2 sin A cos A. sin (A + B) = sin A cos B + cos A sin B cos 2A = cos2 A - sin2 A = 1 - 2 sin2 A = 2 cos2 A - 1. sin (A/2) = ħsqrt(1- cos A)/2. cos (A/2) = ħsqrt(1 + cos A)/2. </p>
Other useful lessons:
Sum and Difference Formulas
Using Double and Half Angle Formulas
Using Sum and Difference Formulas
(Continued from above) Let us see; how to derive the double angle formulas for sine and cosine using their sum formulas:
For an angle with measure A, the double angle formula for sine function is
         sin 2A = 2 sin A cos A.
In the sum formula sin (A + B) = sin A cos B + cos A sin B, on changing B with A in, we'll get double angle formula for sine.
Also the double angle formulas for cosine function are
         cos 2A = cos2 A - sin2 A
                   = 1 - 2 sin2 A
                   = 2 cos2 A - 1.
Similarly, for an angle with measure A, the half angle formula for sine and cosine trigonometric functions are
         sin (A/2) = (1 - cos A)/2.
         cos (A/2) = (1 + cos A)/2.
For example, cos 15 can be evaluated using the formula cos (30/2) = (1 + cos 30)/2, and on substituting cos 30 = 3/2 in this, you'll get {(2 + 3)}/2.
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