Question

Inverse Trig Functions Worksheet, Help Please

Answer 1

They just throw these full speed at ya, eh?

Answer 2

No lol i was taking the class over the summer so i could get it out of the way and i fell behind on my work :p

Answer 3

I just finished a summer session, so I can understand that, lol. Well, where we had for example sin(π/6) = 1/2. What we had was sin of an angle = a number. Well, inverse functions are the opposite. Instead of sin angle number, we have arcsin number = angle.

Answer 4

Wasn't sure if you were typing up something, but yeah. So The first question says sin B = 11/18, find angle B. Well, trig functions use angles to find numbers and inverse trig functions use numbers to find angles. So if sinB = 11/18, then arcsin(11/18) = B

Answer 5

Lol yeah i have like fourteen more of these things all due tomorrow :p but alright, im still kinda confused though

Answer 6

Well, I just realized, but when I say arcsin, inverse sin, theyre both the same thing. So arcsin is the same as sin^-1 (not an actual exponent, just notation), so sorry for the confusion. But alright, so maybe we can think of it this way. Angle and number switch off when you change from trig to inverse trig and vice versa.
sin(angle) = number -> sin^-1(number) = angle
cos^-1(number) = angle -> cos(angle) = number. So given sinB = 11/18, if I want to find B, I need to use inverse sin. Inverse solves for angles. So if I punch in sin^-1 of 11/18 in my calculator, I get answer A.

Answer 7

So i can just use my calculator for this?

Answer 8

Yes, you kind of have to for these problems. And sorry, been hopping back and forth between questions xD

Answer 9

The only thing tricky is sometimes the questions are asking for degree and sometimes theyre askign for radians. These are two different modes on your calculator. If you want an answer in radians, having your calculator set to degrees will give you a way wrong answer, so you need to be careful.

Answer 10

not to many people are going to download and open a file....

Answer 11

also ask one question at a time

Answer 12

Alright, so how do i know what its set on?

Answer 13

can you just ask the first question on the worksheet?

Answer 14

Im not talking to you im talking to @Psymon

Answer 15

ok

Answer 16

I apologize, I ran to the kitchen real quick. And there should be some sort of indication on your calculator that will tell you the current mode youre in. Maybe a small deg or rad appears. If not, then you would need to find a mode button on your calculator and see if you are able to check, Either way, youll need to know how to switch back and forth on your calculator to do all of these problems.

Answer 17

what calculator?

Answer 18

Ok i figured it out lol

Answer 19

Awesome :3

Answer 20

So the second problem wants your answer in radians, so youll need your calculator in that mode. Again, it wants you to find an angle, so you know you have to use inverse. In this case, tanB = .34. So this means in turn that tan^-1(.34) = B. Which is another calculator problem.

Answer 21

I got C for number 2

Answer 22

Right.

Answer 23

Alright, How do go about solving number 3?

Answer 24

Now 3 is obviously a bit different, but youre solving for an angle. Given that, you know its an inverse trig problem. Now its just a matter of picking which inverse trig to use. This requires us to go back to our knowledge of which sides mean which trig function. In reference to angle Y, we have a number that is opposite as well as a number that is on the hypotenuse. So given opposite and hypotenuse, I can choose sin as the trig function I will use since sin of an angle = opp/hyp. So that being said, my angle is Y and my opposite over hypotenuse is 3.5/4.6. So my equation is sinY = (3.5/4.6). To find Y, i switch the values and use sin^-1 instead. so synY = (3.5/4.6) becomes sin^-1(3.5/4.6) = Y. It wants this in degrees, so we need degree mode and then its just calculator work.

Answer 25

also remember that sin^-1(x) has 2 answers on the domain 0<=x<=2pi and infinite answers on the R

Answer 26

and its range is -pi/2 to pi/2

Answer 27

ok I should say that sin(x) = A has infinite answers for x when A is a constant
but inorder for us to make an inverse function we need it to be a function....so we must limit the range of sin^-1(x)

Answer 28

think of sin(x) = 1/2
x = 30,150,390,.....all these are true and infinite more
but
sin^-1(1/2) = 30
not
sin^-1(x) = 30 and 150 and ......
because 30 is in -pi/2 to pi/2

Answer 29

hope this helps, I find the range restriction on sin,cos....to be the most confusing

Answer 30

It will be helpfu later. He's still just using triangles to find values and such. I'm sure we'll get to the point of needing to be aware of domains and ranges and such, but thanks for the input ^_^

Answer 31

Yes thanks for the input. Anyways, sorry i was getting food, but is the answer A?

Answer 32

Yep.

Answer 33

Alright. So that leaves the only questions i need help on are 4,8,9, annd 10

Answer 34

So #4 its best to draw so we can kinda see whats going on.

Answer 35

So the length of the ladder, if you can try to actually imagine it as a triangle, would be the hypotenuse. The distance the base is from the wall would be the length of the bottom, which would be x. So we need to be able to use the information given to solve for x.