Question

Найдите tgx , если sinx=-3/5​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find tg(x) (which is the same as tan(x)), we can use the given information that sin(x) = -3/5.

Recall that the tangent function is defined as the ratio of the sine and cosine functions: tan(x) = sin(x) / cos(x).

Now, we need to find the value of cos(x) to calculate tan(x). To do this, we can use the Pythagorean identity for trigonometric functions: sin^2(x) + cos^2(x) = 1.

Since we know sin(x) = -3/5, we can solve for cos(x):

(-3/5)^2 + cos^2(x) = 1 9/25 + cos^2(x) = 1 cos^2(x) = 1 - 9/25 cos^2(x) = 16/25

Taking the square root of both sides:

cos(x) = ±√(16/25) cos(x) = ±(4/5)

Now, let's determine the sign for cos(x). Since sin(x) = -3/5, and sin(x) is negative in the third and fourth quadrants, we know that cos(x) should be negative in the third quadrant to maintain the negative sign for sin(x). Therefore, cos(x) = -4/5.

Now, we can find tan(x):

tan(x) = sin(x) / cos(x) tan(x) = (-3/5) / (-4/5) tan(x) = (3/5) / (4/5) tan(x) = 3/4

So, tg(x) (or tan(x)) is equal to 3/4.