Question

Найти tgx, если sinx=-3/5 , при

Answer 1

Поскольку π < α < 3π/2 - третья четверть, то в третьей четверти тангенс положителен.

По определению синусa: sin - отношение противолежащего катета к гипотенузе, т.е.

3 - противолежащий катет

5 - гипотенуза

4 - прилежащий катет (найдено по теореме Пифагора)

Тангенс - отношение противолежащего катета к прилежащему катету

tg x = 3/4 - ОТВЕТ

Answer 2

To find the value of tgx (tangent of x) given that sinx = -3/5, we can use the trigonometric identity relating sine and tangent:

tan(x) = sin(x) / cos(x)

Since we know the value of sin(x) as -3/5, we still need to find the value of cos(x) to calculate tgx.

To find cos(x), we can use the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

Substitute the known value of sin(x):

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

Solving for cos(x):

9/25 + cos^2(x) = 1

cos^2(x) = 1 - 9/25

cos^2(x) = 16/25

Taking the square root of both sides (note that cos(x) is positive in the second quadrant where sin(x) is negative):

cos(x) = sqrt(16/25)

cos(x) = 4/5

Now, we can calculate tan(x):

tan(x) = sin(x) / cos(x)

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

Divide the fractions:

tan(x) = -3/4

So, the value of tgx is -3/4.