Question

Sin 10'-sin80'*tg50'​

Answer 1

Ответ:-1

Пошаговое объяснение:  

sin10= cos80             tg50=sin50/cos50

sin 10'-sin80'*tg50=  cos80-sin80sin50/cos50=

=(cos 80 · cos 50 – sin 80 · sin 50)/cos50=cos130/cos50=-cos50/cos50=-1

  cos α · cos β – sin α · sin β   =cos(α + β)

cos130=cos(180-50)=-cos50

Answer 2

To calculate the value of the expression sin 10' - sin 80' * tg 50', we first need to convert the angles from minutes to degrees, as trigonometric functions usually operate with angles in degrees.

1 minute (1') is equal to 1/60 degrees (1/60°).

So, sin 10' becomes sin(10/60°) = sin(1/6°) and sin 80' becomes sin(80/60°) = sin(4/3°).

Similarly, tg 50' becomes tg(50/60°) = tg(5/6°).

Now we can substitute these values into the expression:

sin(1/6°) - sin(4/3°) * tg(5/6°)

However, it's important to note that the trigonometric functions in the given expression are in degrees, not radians. Most programming languages and calculators typically expect trigonometric functions to be in radians, so it's necessary to convert the angles to radians before evaluating the expression.

If you want the answer in degrees, you can evaluate the expression as follows:

sin(1/6°) ≈ 0.00291287 (approximately) sin(4/3°) ≈ 0.0675366 (approximately) tg(5/6°) ≈ 0.00904299 (approximately)

Substituting these values:

0.00291287 - 0.0675366 * 0.00904299 ≈ 0.00291287 - 0.00061229 ≈ 0.00230058 (approximately)

Therefore, sin 10' - sin 80' * tg 50' is approximately 0.00230058 (in degrees).