Question

4sin(-60º) + cos(750º) - 3сtg(150º)

Answer 1

Ответ:

Пошаговое объяснение:

-4sin60+cos(360*2+30)-3ctg(180-30)=

-4*V3/2+cos30+3ctg30=-2V3+V3/2+3*V3=V3+V3/2=3V3/ 2

(V- корень)

Answer 2

Ответ: 4*sin(-60º) + cos(750º) - 3*сtg(150º)=4*(-√3)*0,5+сos(2*360+30)-3*ctg(-30⁰)=-2*√3+0,5*√3-3*√3=-4,5*√3.

Пошаговое объяснение:

Answer 3

To calculate the expression, let's evaluate each trigonometric function individually:

1. 4sin(-60º): The sine function is periodic with a period of 360º. Since sin(-60º) is the same as sin(300º) (adding a full rotation), we can calculate sin(-60º) as sin(300º). The value of sin(300º) is -0.5.

2. cos(750º): The cosine function is also periodic with a period of 360º. To find cos(750º), we can subtract 2 full rotations (720º) from 750º, resulting in 30º. The value of cos(30º) is √3/2.

3. 3сtg(150º): The cotangent function is the reciprocal of the tangent function. To find ctg(150º), we need to calculate tan(150º) and then take its reciprocal. Since tan(150º) = -√3, the reciprocal is -1/√3.

Now, let's substitute these values into the expression and simplify:

4sin(-60º) + cos(750º) - 3сtg(150º) = 4(-0.5) + (√3/2) - 3(-1/√3) = -2 + (√3/2) + (3/√3) = -2 + (√3/2) + (√3/√3) [Multiplying (3/√3) by (√3/√3) to rationalize the denominator] = -2 + (√3/2) + (√3/√3) = -2 + (√3/2) + (√3/√3) = -2 + (√3/2) + (√3/√3) = -2 + (√3/2) + 1 = -2 + (√3/2) + 1 = -1 + (√3/2)

Therefore, the simplified value of the expression 4sin(-60º) + cos(750º) - 3сtg(150º) is -1 + (√3/2).