Question

I need help with this ACT review question.
I already finished this and didn't answer this question. How does one solve this?

Answer 1

Here

Answer 2

Say we have sin x. What's the value x have to be for sin x to reach its maximum (1)?

Answer 3

I have no idea, Geometry was a couple years ago lol. So far I've noticed this type of trig is raping me

Answer 4

Do you remember something about that? sinx is basically height of triangle in unit circle

So what's degree x have to be for this triangle to reach highest possible height?

Answer 5

90?

Answer 6

All I'm thinking in my head is Soh Cah Toa and it doesn't seem to do anything for this lol, sorry I'm so bewildered

Answer 7

@geerky42

Answer 8

@ParthKohli
@phi
@jim_thompson5910
@mathstudent55
@jdoe0001
@zepdrix
@campbell_st

Answer 9

sup? :U

Answer 10

Lol, you up to help me?

Answer 11

So uhhh\[\Large\rm y=\sin2a\]We want the a values that give us \(\Large\rm y=1\) because that's the maximum for the sine function.
And we want the smallest a value which does so.

Where we gettin stuck?
Evaluating specific a's?

So for a=pi/4,
\[\Large\rm y=\sin2 \frac{\pi}{4}\]\[\Large\rm y=\sin\frac{\pi}{2}\]Do you know sin(pi/2)? :O

Answer 12

Alright I did not remember that y=1 part, let's see

Answer 13

Isn't that 1.57...?

Answer 14

Sin(pi/2) ?
No.
Again, remember that the `maximum` of the sine function is 1.
So you should be getting something like 1, or a decimal less than 1.

Answer 15

If you're putting it into the calculator, make sure you're in `radians` mode.

Answer 16

Oh ok, I wasn't even sure what I should have been doing. I put it in the calculator and got 1

Answer 17

Ok great.
So a=pi/4 ended up giving us y=1, yes?

Answer 18

Yes

Answer 19

We're looking for the `smallest` a value that will give us y=1.
So we should check the other ones if they're smaller than pi/4.

Do we have any others that we need to check?
Any other a values smaller than pi/4?

Answer 20

No sir

Answer 21

Mmm ok great!
So it seems a=pi/4 is the correct choice!

That is the smallest a value (among our options) that will maximize the sine function.

Answer 22

Alright so y has to equal 1 for sin, is there something else for the other ones?

Answer 23

y has to equal 1 in order to be a `maximum of the sine function`.

Other what? >.<

Answer 24

Cos, etc?

Answer 25

Cosine also has a maximum of 1.
The other functions beyond that are a little weird though :o