VCE Maths questions help (1 Viewer)

[fluffchuck]

How are you meant to know whether a question asking you to find a sin value, for example, sin 225, is asking for the value in degrees or radians?
Would the same apply for cos and tan?

The value of sin(225) is neither in degrees nor radians.

 

[fluffchuck]

The area of a bushfire, A hectares, t hours after the fire has started is modeled by the rule A = 90t^2 - 3t^3, t > 0
After how many hours does the fire go out
A = 0
90t^2 - 3t^3 = 0
t = 0 and 30

Which answer do i choose? 0 hours or 30 hours?

t = 30, t = 0 is the start of the bushfire.

 

[fluffchuck]

When stating the domain and range, how do you know whether to put ( or [

Using ) or ( means greater than / less than.
Using ] or [ means greater than or equal / less than or equal.

 

[boredsatan]

Is "nor" the same as "and" in probability?

Anyone?

 

[boredsatan]

how do you find the value of cos (-120)?
Urgent, please please help

 

[1729]

how do you find the value of cos (-120)?
Urgent, please please help

cos(-120) = cos(120) = -cos(60) = -1/2

 

[boredsatan]

cos(-120) = cos(120) = -cos(60) = -1/2

thanks

 

[boredsatan]

What is the difference between a general solution and solving for a specified domain in trig equations?

 

[boredsatan]

What is the difference between a general solution and solving for a specified domain in trig equations?

Also, can someone please explain how to find the general solution to the following equations.
Cos 2(x+pi/3) = 1/2

2 tan 2(x+pi/4) = 2√(3)

2 sin(x+pi/3) = -1

Thanks

Silly question, but is
sin 2(x+pi/3) the same as sin(2x+2pi/3)

 

[InteGrand]

Also, can someone please explain how to find the general solution to the following equations.
Cos 2(x+pi/3) = 1/2

2 tan 2(x+pi/4) = 2√(3)

2 sin(x+pi/3) = -1

Thanks

Silly question, but is
sin 2(x+pi/3) the same as sin(2x+2pi/3)

Answer to your last question: yes.

 

[boredsatan]

Answer to your last question: yes.

Thanks. Also, do you know how to find the general solutions to the equations I posted above?
Thanks

 

[InteGrand]

Thanks. Also, do you know how to find the general solutions to the equations I posted above?
Thanks

Yes, I do.

 

[boredsatan]

Yes, I do.

Could you please explain how to do it as read my textbook but got confused with it's explanation

 

[InteGrand]

Also, can someone please explain how to find the general solution to the following equations.
Cos 2(x+pi/3) = 1/2

2 tan 2(x+pi/4) = 2√(3)

2 sin(x+pi/3) = -1

Thanks

Silly question, but is
sin 2(x+pi/3) the same as sin(2x+2pi/3)

Could you please explain how to do it as read my textbook but got confused with it's explanation

 

[boredsatan]

If (x-1)^3 = 8
then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
And how would you work out the value of the base?

How would you find the basic angle for a negative value?
For instance cos(x) = -1/2

How would you work out (x+1)^3 = -2 without a calculator?
Thanks

 

[boredsatan]

If (x-1)^3 = 8
then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
And how would you work out the value of the base?

How would you find the basic angle for a negative value?
For instance cos(x) = -1/2

How would you work out (x+1)^3 = -2 without a calculator?
Thanks

Anyone?

 

[boredsatan]

Bump!
Any one know how to do the above questions?

Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
I'm confused with the negative domain
Thanks

 

[boredsatan]

Bump
Can somebody PLEASE ANSWER all my questions above?

 

[fan96]

Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
I'm confused with the negative domain
Thanks

The sine wave has symmetry across the origin, so it's an odd function, which means that .

Basically that implies that the sine of a negative angle is the same as reversing the sign of the sine of the positive angle, i.e.

.

When we go in the positive direction, the first angle for which is .

So that means that when we go in the negative direction, the first angle for which is .

But is outside the range of , so it's not a solution to the equation.

 

[fan96]

Also, does anyone know how you would work out sin(11pi/4)

The period of is . So,



Also, . So,

How would you work out (x+1)^3 = -2 without a calculator?
Thanks

If you want the answer in exact form, then