sin and sin^-1????

Question

OK, I admit that I don't know much about calculators especially the TI-84 Silver edition.

here the question

during a hurricane, a 37 foot tree breaks at the base and falls against a nearby building. The top of the tree now stands 12ft above the ground. Find the angle between the ground and the base of the tree.

OK, so I use sin to find the angle, right?

it would be sin(12/37) but when I plug the number in it gives me a very ridiculus number.
when I press sin^-1(12/37) I got the result?
why and when will press sin^-1 instead of sin?????

when will I use sine and sine^1 ( or whatever it is)
I have never learn these things though.

in other words, sine is for angle while sine^1 is for sides to find the angle

Answer 1

You're confusing how sine works. You don't take the sine of SIDES of a triangle. You take the sine of a ANGLE. So if θ is the angle between the base of the tree and the ground, then what you end up with here is
sin(θ) = opposite/hypotenuse = 12/37.

You want to know what θ is given the fact that sin(θ) = 12/37. In this case then you want the INVERSE SINE of (12/37). Sin^-1(12/37) means "the sine of what angle is 12/37?".

Note that sin^-1(θ) is NOT 1 / sin(θ). Although you have a -1 exponent here, that is the special notation for inverse trig functions.

Answer 2

You are supposed to use sin^-1. This is known as the inverse sine.

The equation you set up to solve this problem would be:

sin (angle) = 12/37

An inverse sine cancels out the sine, so you can get the angle by itself in this function.

So when you take the inverse sine, you will obtain:

sin^-1 (sin (A)) = sin^-1 12/37

Since sin and sin^-1 cancel out, you're left with

A = sin^-1 12/37
which is approximately 19 degrees.

As a general rule of thumb, you use the inverse sine, or any inverse trig function to solve for an angle, while you use sine to calculate one of the sides when you're given the angle.

Answer 3

You were given that sin (x) = 12/37.
To solve this for x, you take the inverse sine of both sides of the equation.
The inverse sine of (sin (x)) equals, of course, x.
The inverse sine of 12/37 = the angle that has a sine of 12/37.

sin (12/37) = the sine of an angle less than one degree. That's not what you want at all.

Answer 4

No.

The sine of the angle is equal to the ratio of the length of the opposite side over the length of the hypoteneuse.

Or:

sin(angle) = 12/37

arcsin(sin(angle)) = arcsin(12/37)

angle = arcsin(12/37)

angle = 19 degrees (approximately)

I hope that helps.

Answer 5

when you are solving for an angle you will use sin^-1, when you are given the angle and need to use it you will use sin

Answer 6

yes, you have to use, in this case, sin^-1 (12/37) which gives you 18.9 degrees

Answer 7

that is correct...but you need to make sure you go to "mode" and make sure that you are in degrees..."deg" and not radians.... "rad"

Answer 8

could you please repeat that, yikes