Question

Чему равен sinα, cosα, tgα при α=600?

Answer 1

Ответ:

Объяснение:

sin600 = sin(240) = sin(180 + 60) = -sin(60) = -$\frac{\sqrt{3}}{2}$
cos600 = cos(240) = cos(180 + 60) = -cos(60) = -$\frac{1}{2}$
tg600 = $\frac{sin600}{cos600}$ => $\frac{\frac{\sqrt{3} }{2} }{\frac{1}{2} }$= $\sqrt{3}$

Answer 2

Trigonometric Functions at α = 600

To find the values of sinα, cosα, and tgα when α = 600, we can refer to the trigonometric definitions and formulas.

1. sinα (sine of α): - The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. - However, since α = 600, which is not within the range of a standard unit circle, we need to convert it to an angle within the unit circle. - By subtracting multiples of 360 degrees from α, we can find an equivalent angle within the unit circle. - α = 600 - 360 = 240 degrees. - Now we can find the value of sinα at α = 240. - According to the trigonometric definitions, sinα = y/r, where y is the length of the side opposite the angle and r is the length of the hypotenuse. - Since α = 240 degrees, we can refer to the trigonometric values for this angle. - sinα = sin(240) = -0.866.

2. cosα (cosine of α): - The cosine function relates the ratio of the length of the side adjacent to an angle to the length of the hypotenuse in a right triangle. - Similarly, we need to convert α = 600 to an angle within the unit circle. - α = 600 - 360 = 240 degrees. - Now we can find the value of cosα at α = 240. - According to the trigonometric definitions, cosα = x/r, where x is the length of the side adjacent to the angle and r is the length of the hypotenuse. - Since α = 240 degrees, we can refer to the trigonometric values for this angle. - cosα = cos(240) = -0.5.

3. tgα (tangent of α): - The tangent function relates the ratio of the sine of an angle to the cosine of the same angle. - We can calculate tgα using the formula tgα = sinα/cosα. - Substituting the values we found earlier, tgα = -0.866 / -0.5 = 1.732. - tgα = 1.732.

Therefore, when α = 600, sinα = -0.866, cosα = -0.5, and tgα = 1.732.

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