Question

Cos a= 1/2 sin a=? ctg a=?

Answer 1

По основному тригонометрическому тождеству "сумма квадрата синуса и косинуса равна 1" найдём синус


Sin<a = корень из (1 - cos квадрат)
=корень из ( 1 - 1/4)
= корень из 3/4
= корень из 3 деленное на два


tg= sin / cos
= 2 корня из 3 / 2
= корень из трех

Котангенс вроде обратен тангенсу значит 1/корень из 3

Answer 2

To find the values of $\sin(a)$ and $\cot(a)$ given that $\cos(a) = \frac{1}{2}$, we can use the Pythagorean trigonometric identity $\sin^2(a) + \cos^2(a) = 1$ and the reciprocal trigonometric identity $\cot(a) = \frac{1}{\tan(a)}$.

Step 1: Find $\sin(a)$. We know that $\cos(a) = \frac{1}{2}$. Using the Pythagorean identity, we have: $\sin^2(a) + \left(\frac{1}{2}\right)^2 = 1$ $\sin^2(a) + \frac{1}{4} = 1$ $\sin^2(a) = 1 - \frac{1}{4}$ $\sin^2(a) = \frac{3}{4}$

Now, taking the square root of both sides (since $\sin(a)$ is positive in the first quadrant), we get: $\sin(a) = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$

Step 2: Find $\cot(a)$. We know that $\cot(a) = \frac{1}{\tan(a)}$. Using the identity $\tan(a) = \frac{\sin(a)}{\cos(a)}$, we can find $\cot(a)$: $\tan(a) = \frac{\sin(a)}{\cos(a)} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

Now, $\cot(a) = \frac{1}{\tan(a)} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$.

So, the values are: $\sin(a) = \frac{\sqrt{3}}{2}$ $\cot(a) = \frac{\sqrt{3}}{3}$