easy trig questions i can't figure out! help!

[msu08]

from crack dat math

1)what is the value of (sin pi/3)(tan-3pi/4) answer is sqrt3/2 i understand sin pi/3 is sqrt 3/2 but how is tan-3pi/4 = 1? i know tan pi/4 is 1.... any help? i'm terrible at trig.

2) cos 7 pi/4 + sin 7 pi/4

don't know how to do this one...

3) cos(pi + 301 pi/2)
they simplify to = pi + 75*2pi + pi/2 then somehow simplify to pi + pi/2=0...but what happened to the 75*2pi? again any help is appreciated!

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[Streetwolf]

from crack dat math

1)what is the value of (sin pi/3)(tan-3pi/4) answer is sqrt3/2 i understand sin pi/3 is sqrt 3/2 but how is tan-3pi/4 = 1? i know tan pi/4 is 1.... any help? i'm terrible at trig.

2) cos 7 pi/4 + sin 7 pi/4

don't know how to do this one...

3) cos(pi + 301 pi/2)
they simplify to = pi + 75*2pi + pi/2 then somehow simplify to pi + pi/2=0...but what happened to the 75*2pi? again any help is appreciated!

1) tan -3pi/4 is just sin(-3pi/4) / cos(-3pi/4). If you think about the circle (and remember you are traveling CLOCKWISE since it's negative), you'll end up in the third quadrant. That means sin and cos are both -sqrt(2) / 2. So since they're the same value, you get 1 when you divide them.

2) cos (7pi/4) is in the 4th quadrant. Notice that 8pi/4 is the same as 2pi so we're really just pi/4 away from a full 360 degrees. Since it's the 4th quadrant and it's cosine, it must be +sqrt(2)/2. Remember that all (n*pi)/4 with n = an odd integer are sqrt(2)/2, either + or -. Same for sine. But 4th quadrant for sine = negative value. So you end up getting sqrt(2)/2 - sqrt(2)/2 = 0.

3) 75*2pi disappears because this just makes you circle around 75 full times. Every 2pi is one full period. So cos(4) is the same as cos (4+2pi) which is the same as cos(4+4pi). You're in the same spot except you've just cycled around one or more times. In this case, 75 full times. After those 75 times you are left with an additional 3pi/2. That's what you need to solve - cos(3pi/2).