Please help me! i do t know....

Mathematics

1 answer:

Karolina [17]2 years ago

4 0

Answer:

$-3/\sqrt{58}$

Step-by-step explanation:

tan = opposite / adjacent

opposite side is the y-coordinate of a point on the terminal side

adjacent side is the x-coordinate of a point on the terminal side

if the terminal side is in the second quadrant (the top-left quadrant), a coordinate on the terminal side would have a negative x-coordinate and a positive y-coordinate

This being the case:

the opposite side (y) would be -3 and the adjacent side (x) would be 7

using the Pythagorean theorem:

$a^2+b^2=c^2$

$7^2+(-3)^2=c^2$

The hypotenuse is c, so it equals $\sqrt{58}$

sin = opposite / hypotenuse

so sin(theta) = $-3/\sqrt{58}$

You might be interested in

Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)

aleksandr82 [10.1K]

$\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}$

Notice that if $f(x)=e^{\sin x}$ , then $f(\pi)=e^{\sin\pi}=e^0=1$ . Recall the definition of the derivative of a function $f(x)$ at a point $x=c$ :

$f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$

So the value of this limit is exactly the value of the derivative of $f(x)=e^{\sin x}$ at $x=\pi$ .

You have

$f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1$