More Math, this time, PreCalculus.

[Goldenboko]

Okay, a question on a test I'm going to take today reads something like Simplify the following =
tan325-tan25
1-tan325tan25

I'd just go:
tan(325-25)
tan300

And that'd be the answer right?

[qwertysaur]

You can go further than that Boko.

From tan(300) you can break it into sin(300)/cos(300)
sin(300) = -sin(60) = √(3)/2
cos(300) = cos(60) = 1/2

So you get (-√(3)/2)/(1/2) = -√(3)

You can remember that tan(60) = √(3) and skip the sin and cos stuff
. Just remember 300 is in quadrant IV so sin and tan is negative. cos is positive in quadrant IV.

[blackmage_nuke]

Okay, a question on a test I'm going to take today reads something like Simplify the following =
tan325-tan25
1-tan325tan25

I'd just go:
tan(325-25)
tan300

And that'd be the answer right?

Wait!!! For that to work wouldnt it have to be
tanA - tanB
1 + tanAtanB
emphasis on the +

So for your problem I would first change all the tan's into sin/cos

So up the top we get

sin325/cos325 - sin25/cos25

which simplifies to

(sin325cos25-sin25cos325) / cos325cos25

then becoming

(sin 325-25) / cos325cos25

and thus

(sin 300) / cos325cos25 (part1)

down the bottom we get

1 - (sin325sin25) / (cos325cos25)

Which converts to

(cos325cos25 - sin325sin25) / (cos325cos25)

making cos(325 + 25) / (cos325cos25)

making cos(350) / (cos325cos25) (part2)

and so when we put part 1 over part 2 the cos325cos25 cancels leaving us with

sin(300)/cos(350)

From there sin300 can be made into -sin60 as sin is negative in the 4th quadrant and cos350 can be made cos10 as cos is positive in the 4th quadrant

-sin60 = -sqrt3/2

so we get to

(-sqrt3) / 2cos10

I dont know what to do about cos 10

Of course if that initial - was a typo Ive just wasted precious minutes in which case i advise that in the future you shouldnt be so negative hohoho pun!!

[Goldenboko]

You can go further than that Boko.

From tan(300) you can break it into sin(300)/cos(300)
sin(300) = -sin(60) = √(3)/2
cos(300) = cos(60) = 1/2

So you get (-√(3)/2)/(1/2) = -√(3)

You can remember that tan(60) = √(3) and skip the sin and cos stuff
. Just remember 300 is in quadrant IV so sin and tan is negative. cos is positive in quadrant IV.

I accidentally reversed that on the test... and got √(3)/3 instead of just √(3).

Dammit. ;-;