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anemone
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Without the help of calculator, evaluate $\cos \dfrac{\pi}{7}\cos \dfrac{2\pi}{7}\cos \dfrac{4\pi}{7}$.
anemone said:Without the help of calculator, evaluate $\cos \dfrac{\pi}{7}\cos \dfrac{2\pi}{7}\cos \dfrac{4\pi}{7}$.
A trigonometric expression is a mathematical expression that involves trigonometric functions, such as sine, cosine, and tangent, as well as variables and constants. It is used to represent relationships between angles and sides of a triangle.
To evaluate a trigonometric expression, you need to substitute the given values for the variables and then use the trigonometric functions to solve for the resulting numerical expression. Make sure to use the correct order of operations and to simplify the expression as much as possible.
Some common trigonometric identities used to evaluate expressions include the Pythagorean identities (sin²x + cos²x = 1, tan²x + 1 = sec²x, 1 + cot²x = csc²x), the double angle identities (sin2x = 2sinx cosx, cos2x = cos²x - sin²x), and the sum and difference identities (sin(x ± y) = sinx cosy ± cosx siny, cos(x ± y) = cosx cosy ∓ sinx siny).
Some tips for simplifying trigonometric expressions include factoring out common factors, using trigonometric identities, converting all trigonometric functions to sine and cosine, and substituting values for trigonometric functions using the unit circle.
Trigonometric expressions are used in various fields such as engineering, physics, and astronomy to solve problems involving angles and distances. They are also used in navigation, surveying, and architecture to calculate distances and angles between objects.