Question

4sim(-60⁰) -3ctg(-60⁰) +5cos(-30⁰)

Answer 1

1. 4sin(-60°)-3ctg(-60°)+5cos(-30°)=-4sin60°+3ctg60⁰+5cos30⁰=-4·√3/2+3·√3/3+5·√3/2=-2√3+√3+2.5√3=1,5√3

Answer 2

To calculate the value of the expression 4sin(-60°) - 3cot(-60°) + 5cos(-30°), you can use trigonometric identities and values for the sine, cosine, and cotangent of standard angles.

1. First, let's find the values of sin(-60°), cos(-30°), and cot(-60°):

• sin(-60°) = -sin(60°) = -√3/2
• cos(-30°) = cos(30°) = √3/2
• cot(-60°) = cot(60°) = 1/tan(60°) = 1/√3

2. Now, substitute these values into the expression:

4sin(-60°) - 3cot(-60°) + 5cos(-30°) = 4(-√3/2) - 3(1/√3) + 5(√3/2)

3. Calculate each term separately:

= -2√3 - √3 + 5√3/2

4. Combine like terms:

= (-2√3 - √3) + 5√3/2 = -3√3 + 5√3/2

5. Finally, simplify the expression:

= (-6√3/2 + 5√3/2) = -1√3/2

So, the value of the expression 4sin(-60°) - 3cot(-60°) + 5cos(-30°) is -√3/2 or approximately -0.866.