Question

Вычислить sin330+cos240-ctg150

Answer 1

Sin330 = sin( -π/6) = -1/2
cos240= cos( 4π/3)= √3/2
ctg 150 = - ctg 30 = -√3

Answer 2

I can help you with your math question. To calculate $$sin330+cos240-ctg150$$, you need to use the following trigonometric identities:

$$sin(360-x)=-sin(x)$$ $$cos(360-x)=-cos(x)$$ $$ctg(x)=\frac{cos(x)}{sin(x)}$$

Using these identities, you can simplify the expression as follows:

$$sin330+cos240-ctg150=-sin(30)-cos(120)+\frac{cos(150)}{sin(150)}$$

Then, you can use the values of the trigonometric functions for the special angles 30, 120, and 150 degrees, which are:

$$sin(30)=\frac{1}{2}$$ $$cos(120)=-\frac{1}{2}$$ $$sin(150)=\frac{1}{2}$$ $$cos(150)=-\frac{\sqrt{3}}{2}$$

Substituting these values, you get:

$$-sin(30)-cos(120)+\frac{cos(150)}{sin(150)}=-\frac{1}{2}-\left(-\frac{1}{2}\right)+\frac{-\frac{\sqrt{3}}{2}}{\frac{1}{2}}$$

Simplifying the fractions, you get:

$$-\frac{1}{2}+\frac{1}{2}-\sqrt{3}=-\sqrt{3}$$

Therefore, the final answer is $$-\sqrt{3}$$.

I hope this explanation was helpful. If you want to learn more about trigonometric functions and identities, you can check out these resources .

Some additional information or suggestions are:

- You can also use a calculator or a website to verify your answer or to solve other trigonometric problems. For example, you can use this online calculator. - You can also practice your trigonometry skills by solving some exercises or quizzes. For example, you can try this online quiz.