Question

ВАРИАНТ 2 3. Найдите значение sina, tga и ctga, если cos a =18/25

Answer 1

To find the values of sine (sin a), tangent (tan a), and cotangent (cot a) given that cos a = 18/25, we'll use trigonometric identities and the Pythagorean identity.

First, let's use the Pythagorean identity for cosine and sine: $\cos^2 a + \sin^2 a = 1$

Given that $\cos a = \frac{18}{25}$, we can solve for $\sin a$: $\sin^2 a = 1 - \cos^2 a$ $\sin^2 a = 1 - \left(\frac{18}{25}\right)^2$ $\sin a = \pm \sqrt{1 - \left(\frac{18}{25}\right)^2}$

Since we're dealing with sine, we'll take the positive square root to get the principal value: $\sin a = \frac{7}{25}$

Next, let's calculate tangent (tan a) using the definition: $\tan a = \frac{\sin a}{\cos a}$ $\tan a = \frac{\frac{7}{25}}{\frac{18}{25}}$ $\tan a = \frac{7}{18}$

Lastly, let's calculate cotangent (cot a) using the reciprocal of tangent: $\cot a = \frac{1}{\tan a}$ $\cot a = \frac{1}{\frac{7}{18}}$ $\cot a = \frac{18}{7}$

So, the values are: $\sin a = \frac{7}{25}$ $\tan a = \frac{7}{18}$ $\cot a = \frac{18}{7}$