Question

Приведите к значениям тригонаметрих функций наименьшего положительного аргумента. 1.Tg=532 2.Cos=20pi/7. P.S. Заранее спасибо)

Answer 1

Tg532=tg(3*180-8)=tg(-8)=-tg8
cos20π/7=cos(3π-π/7)=cos(π-π/7)=-cosπ/7

Answer 2

Trigonometric Functions and Their Values

The trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Each of these functions has a range of values that they can take, depending on the angle.

1. Tangent (tan): The tangent function is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. The value of the tangent function can be positive, negative, or zero, depending on the angle. For the smallest positive argument, the tangent function can take any value between negative infinity and positive infinity.

2. Cosine (cos): The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. The value of the cosine function can range from -1 to 1. For the smallest positive argument, the cosine function can take any value between -1 and 1.

Now, let's look at the specific values you provided:

1. Tangent (tan): You mentioned that the tangent function has a value of 532. However, the tangent function can only take values between negative infinity and positive infinity. Therefore, the value you provided (532) is not a valid value for the tangent function.

2. Cosine (cos): You mentioned that the cosine function has a value of 20π/7. The value of the cosine function can range from -1 to 1. To determine the value of the cosine function for the given argument, we need to evaluate the expression 20π/7. By calculating this expression, we find that the value of the cosine function for an argument of 20π/7 is approximately -0.6235.

Please note that the values provided for the tangent and cosine functions are not valid for the smallest positive argument. The tangent function can take any value between negative infinity and positive infinity, while the cosine function can take any value between -1 and 1.