Without using table, what is the value of tan 3465 degree?

[ugu]

Answer:

tan 3465 degree = tan 45 = 1

right?

 

[Dr.Peterson]

Answer:

tan 3465 degree = tan 45 = 1

right?

Is there a reason you're unsure?

I would show a little more work to explain why those should be equal. Then I'd be certain!

 

[ugu]

somehow

 

[BigBeachBanana]

somehow

When is tan(x)=1 on the unit circle?

 

[Dr.Peterson]

somehow

Are you saying you just guessed??

What angle between 0 and 360 degrees is coterminal with 3465 degrees? What other angle has the same tangent?

 

[Deleted member 4993]

Answer:

tan 3465 degree = tan 45 = 1

right?

tan(Θ) = tan(Θ ± n * π)

 

[pka]

[imath][3465(\mod~360)=245[/imath] See here


[imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath]

 

[BigBeachBanana]

\

[imath][3465(\mod~360)=245[/imath] See here


[imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath]

Why mod 360 and not 180?

 

[Harry_the_cat]

[imath][3465(\mod~360)=245[/imath] See here


[imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath]

225 not 245 pka

 

[Harry_the_cat]

\

Why mod 360 and not 180?

either / or

 

[BigBeachBanana]

either / or

The solutions exist in the first and third quadrant of the unit circle. Mod 360 only provide the solution in the first quadrant, either/or third, but not both.
The OP's goal was to show tan(3645)=tan(45).
3465 mod 180 = 45

 

[Harry_the_cat]

The solutions exist in the first and third quadrant of the unit circle. Mod 360 only provide the solution in the first quadrant, either/or third, but not both.
The OP's goal was to show tan(3645)=tan(45).
3465 mod 180 = 45

Yeah sure but 3465 (mod 360) = 225 and it's only one more step to say that \(\displaystyle tan 225\degree = tan 45\degree\).

mod 360 will lead to the answer for sin and cos as well, mod 180 won't.

 

[BigBeachBanana]

mod 360 will lead to the answer for sin and cos as well, mod 180 won't.

It's because sin(x) and cos(x) have a period of [imath]2\pi = 360 \degree[/imath] and tan(x) has a period of [imath]\pi = 180\degree ?[/imath]

 

[Harry_the_cat]

It's because sin(x) and cos(x) have a period of [imath]2\pi = 360 \degree[/imath] and tan(x) has a period of [imath]\pi = 180\degree ?[/imath]

Yes, but my point was you can use mod 360 in all cases, but mod 180 only for tan. Trying to keep it simple.