Can you solve the given problems?

Question

Here are some math problems i need help solving... ive been trying to solve ones like these but just dont undersand it and my brain completely turned off from about a billion others like these.

1.The perimiter of a circle equals 6 pi, what is the area of the circle?

2. A race track has 1km, a bike weel has a radius of .5 m. How many turns does the wheel have to make to go around the track?

3. Simplify:
(1-sin^2 a)
over =
1- cos^2 a

4. Simplify:
tg a * cos a

5.Simplify:
1 + tg^2 a

6.Simplify:
(1 - sin a) * (1+sin a)
OVER
(sin a) * (cos a)

7. Solve:
tg 60
OVER - sqrt of 3
ctg 45 - sin 30

8. Solve:
sin 30 + cos^2 45
OVER
2 - tg 45

9. Solve:
4 cos 60 - 3tg^2 30
OVER - ctg 45
sin 45 * cos 45

10. Solve:
sin 30 * cos 30 * tg 30 * ctg 30

Like i said, these are just more quesions from a series of plenty ive already done, i can not ask my teacher for help anymore as it is due tomorrow and im exhausted so im looking for help, not trying to get away without doing it. And yes i know it is saturday tomorrow.

Answer 1

I am doing a few for you.You may contact me through yahoo Answers when you require solutions of many a problems
tg a*cosa
=(sin a/cosa)cosa
sin a
5.1+tg^2a
=1+(sin^2a/cos^2a)
=(cos^2a+sin^2a)/cos^2a
=1/cos^a
=sec^2a
6.Numerator=(1+sin a)(1-sin a)
=1-sin^2a [applying (a+b)(a-b)=a^2-b^2 formula]
=cos^2 a
Numertor/denominator
=cos^2a/sina*cosa
=cos a/sin a
=cot a

Answer 2

1. Perimeter = 2*PI*radius 6*PI = means radius = 3
2. 1000/PI
3. cos^2a/sin^2a

I'm not up on my trig identities any more. Start from the definition of tangent and remember that sin^2a = 1 - cos^2a and vice versa.

Answer 3

4. tg a * cos a = tan(a)*cos(a) = sin(a)/cos(a) * cos(a) = sin(a)

5. 1 + tan^2(a) = 1 + sin^2(a)/cos^2(a) = [cos^2(a) + sin^2(a)]/cos^2(a) = 1/cos^2(a) = csc^2(a)

6. {(1 - sin a) * (1+sin a)}/{(sin a) * (cos a)}
(1 - sin a) * (1+sin a) = 1 - sin^2(a), but remember that sin^2(a) + cos^2(a) = 1, therefore, 1-sin^2(a) = cos^2(a)

cos^2(a)/sina*cosa = cos(a)/sin(a) = cot(a)

Answer 4

I know the answers to all...
but..you know what...its called homework...if you dont do it yourself..you will never learn..and you will fail your math test...maybe you could ask your teacher to help you with them?