# Thread: VCE Maths questions help

1. ## Re: VCE Maths questions help

evaluate tan (2pi/3)
= (3pi/3) - (pi/3)
=(pi) - (pi/3)
=+ tan (pi/3) = (√3)
Is this correct?

2. ## Re: VCE Maths questions help

why is cos (-pi/4) the same as cos (pi/4)?

3. ## Re: VCE Maths questions help

Originally Posted by boredsatan
evaluate tan (2pi/3)
= (3pi/3) - (pi/3)
=(pi) - (pi/3)
=+ tan (pi/3) = (√3)
Is this correct?
Not sure what you've done in the second line, but that seems unnecessary for that question anyway. Using angles of any magnitude, you know tan(2pi/3) is in the second quadrant, which is negative for tan.

So tan(2pi/3) = -tan(pi/3) = -√3

4. ## Re: VCE Maths questions help

Originally Posted by Sp3ctre
Not sure what you've done in the second line, but that seems unnecessary for that question anyway. Using angles of any magnitude, you know tan(2pi/3) is in the second quadrant, which is negative for tan.

So tan(2pi/3) = -tan(pi/3) = -√3
Thanks!
also, do you know why is cos (-pi/4) the same as cos (pi/4)?

5. ## Re: VCE Maths questions help

The first four quadrants are positive for cos. (pi/4) is obviously in the first quadrant, and if you can see that (-pi/4) is actually in the fourth quadrant, then both cos(pi/4) and cos(-pi/4) are positive (1/√2). It might not be the best explanation because this is much easier to show with a diagram of the quadrants, but I hope it helps anyway.

6. ## Re: VCE Maths questions help

If pr(A) = 0.45, pr(B) = 0.35, and pr(A inverted u B) = 0.25, how would you find Pr (A' inverted u B')

7. ## Re: VCE Maths questions help

convert 7pi/12 to degrees
(7pi/12)*(180/pi)
=1260pi/12pi
= 105
is this correct?

8. ## Re: VCE Maths questions help

Originally Posted by boredsatan
convert 7pi/12 to degrees
(7pi/12)*(180/pi)
=1260pi/12pi
= 105
is this correct?
anyone?

9. ## Re: VCE Maths questions help

Anyone know how to work out tan (5pi/4) as i'm really confused?

bump

11. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Anyone know how to work out tan (5pi/4) as i'm really confused?
yeah the exact value is sqrt(6Pi/9)

12. ## Re: VCE Maths questions help

Originally Posted by boredsatan
Anyone know how to work out tan (5pi/4) as i'm really confused?
tan(5pi/4) = tan(pi/4 + pi)
= (tanpi + tan(pi/4))/(1-tanpi*tan(pi/4))
= (0+1)/(1-0)
= 1

13. ## Re: VCE Maths questions help

Originally Posted by pikachu975
tan(5pi/4) = tan(pi/4 + pi)
= (tanpi + tan(pi/4))/(1-tanpi*tan(pi/4))
= (0+1)/(1-0)
= 1
pikachu: more directly this way:

tan(pi/4 + pi) = tan(pi/4) = 1

14. ## Re: VCE Maths questions help

How would you work out tan (-2pi/3)
I'm confused as it's negative

15. ## Re: VCE Maths questions help

Originally Posted by boredsatan
How would you work out tan (-2pi/3)
I'm confused as it's negative
It's in the 3rd quadrant so it's positive since tan is positive in the third quadrant.

tan(pi/3) = tan(-2pi/3) = sqrt3

16. ## Re: VCE Maths questions help

in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
draw a venn diagram
how do you work out how many people speak both french and german, given that it's not stated above?

bump

18. ## Re: VCE Maths questions help

solve cos(x) = 0.5, (-4pi to 4pi)
base = pi/3,
+ve rotation
x = pi/3, 2pi-pi/3 = 5pi/3
pi/3 + 2pi = 7pi/3
5pi/3 + 2pi = 11pi/3

-ve rotation
x = -pi/3, x = -2pi + pi/3 = -5pi/3
-2pi - (-pi/3) = -5pi/3
-2pi - (-5pi/3) = -pi/3

19. ## Re: VCE Maths questions help

Originally Posted by boredsatan
solve cos(x) = 0.5, (-4pi to 4pi)
base = pi/3,
+ve rotation
x = pi/3, 2pi-pi/3 = 5pi/3
pi/3 + 2pi = 7pi/3
5pi/3 + 2pi = 11pi/3

-ve rotation
x = -pi/3, x = -2pi + pi/3 = -5pi/3
-2pi - (-pi/3) = -5pi/3
-2pi - (-5pi/3) = -pi/3

cos(x) is an even function so cos(x) = cos(-x). If you have 7pi/3 and 11pi/3, you must also have -7pi/3 and -11pi/3.

20. ## Re: VCE Maths questions help

Originally Posted by boredsatan
in a population of 10,000 people, 75% spoke german, 45% spoke french, and 10% of the population did not speak either french or german
draw a venn diagram
how do you work out how many people speak both french and german, given that it's not stated above?
10,000 people
7,500 German
4,500 French
1,000 Neither

If N people speak both,
(7500 - N) + (4500 - N) + N + 1000 = 10000
N = 3000 people

21. ## Re: VCE Maths questions help

A is a matrix of order (3*5) and the order of the matrix product AB is (3*1) then what is the order of matrix B? How would you work it out?

22. ## Re: VCE Maths questions help

Originally Posted by boredsatan
A is a matrix of order (3*5) and the order of the matrix product AB is (3*1) then what is the order of matrix B? How would you work it out?
Remember, the general rule is if A is (m x n) and B is (n x p), then AB is (m x p).

Since A is (3 x 5) and AB is (3 x 1), we must have that B is (5 x 1). (No. of rows of B must be 5 in order for B to be compatible with A in the product AB, and no. of columns of B must be 1 in order that the no. of columns in the result AB is 1.)

23. ## Re: VCE Maths questions help

Originally Posted by boredsatan
If pr(A) = 0.45, pr(B) = 0.35, and pr(A inverted u B) = 0.25, how would you find Pr (A' inverted u B')
It helps if you draw a venn diagram or you can alternatively use de Morgan's Laws

24. ## Re: VCE Maths questions help

Originally Posted by BenHowe
It helps if you draw a venn diagram or you can alternatively use de Morgan's Laws
Thanks for replying to my post which was over a month ago!

25. ## Re: VCE Maths questions help

2^x = 7
How would you solve for x without a calculator using logarithms?

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