Question

что такое : sin cos tg и как их найти

Answer 1

синус острого угла прямугольного треугольника - отношение противолежащей стороны к гипотенузе

косинус острого угла прямугольного треугольника - отношение прилежащей стороны к гипотенузе

тангенс острого угла прямугольного треугольника - отношение противолежащей стороны к прилежащей

к примеру треугольник ABC угол A=90

sin B=AC/BC

cos B=AB/BC

tg B=AC/AB

 

Answer 2

Understanding Trigonometric Functions

Sin, Cos, and Tan (Tg) are fundamental trigonometric functions used to relate the angles of a triangle to the lengths of its sides. Here's a brief overview of each function and how to find them:

1. Sin (Sine): - The sine of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. - It is denoted as sin θ, where θ is the angle. - The formula to find sin θ is: sin θ = opposite/hypotenuse.

2. Cos (Cosine): - The cosine of an angle in a right-angled triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. - It is denoted as cos θ, where θ is the angle. - The formula to find cos θ is: cos θ = adjacent/hypotenuse.

3. Tan (Tangent): - The tangent of an angle in a right-angled triangle is the ratio of the length of the side opposite the angle to the length of the adjacent side. - It is denoted as tan θ, where θ is the angle. - The formula to find tan θ is: tan θ = opposite/adjacent.

Finding Trigonometric Functions

To find these trigonometric functions, you can use the following formulas:

- For sine and cosine: - \(\frac{sin a}{cos a} = \frac{b}{a}\). - \(\frac{cos a}{sin a} = \frac{a}{b}\).

- For tangent: - \(tg x = \frac{sin x}{cos x}\). - \(tg x = \frac{cos x}{sin x}\). - \(\frac{cos x}{sin x} = ctg x\). - \(tg x = \frac{1}{tg x}\). - \(tg x = \frac{1}{ctg x}\).

These formulas provide a systematic way to calculate the trigonometric functions for a given angle or sides of a right-angled triangle.

If you have specific values for the sides of a right-angled triangle or the measure of an angle, you can use these formulas to find the sine, cosine, and tangent of the angle.

Feel free to ask if you have further questions or need more examples!