math questions!! urgent!!?

Question

i have an entrance test coming up and i just need to know the ff:
1. sine/cosine/tangent: how to determine which one is opposite and adjacent
2. when exactly do you apply sine rule and cosine rule?
3. is there a way of solving a sine/cosine/tangent of a number without using a calculator (algebraically)? how?
4. Statistics and probability: What are complementary events and mutually exclusive events?
5. Logarithms: can you find a log of a number without using a calculator (algebraically)?

Please... I hope you can answer in the next 30 mins. I am not allowed to use graphing calculator in the test that's why i'm panicking. Thanks to those who answer.

you could also add any formulas for science. Anything you can think of for chemistry or physics that you think that could help me in my test. The thing is, even I don't know what's gonna be in it, so I have to study everything. Thanks

Answer 1

First of all stop panicking....
1) Use SOH CAH TOA to determine which angle is opposite and adjacent. SOH = sin = opposite/hypotenuse CAH = cosine = adjacent/hypotenuse and TOA = tangent = opposite/adjacent. The rest are easy: secant is the opposite ofcosine, cosecant is the opposite of sine, and cotanget is the opposite ofr tangent.
2) Whenever you have side side side you should apply the cosine rule. Whenever you have AAA angle angle angle you should apply the sine rule.
3) Yes there is a way, and that is using the unit circle. If the teacher does not allow the unit circle then you have to memorize the sine, and cosine for the basic angles: 30,45,90. Hence if they give you an angle in the third quadrant you simply subtract from 180 to find the reference angle (30,45,60,90). If the angle they ask for is in the fourth quadrant then you have to subtract from 360.
4)Mutually exclusive events are those that the probability of one event does not affect the probability of another event. LIke say a marble drawn from a bag. The second time the second marble picked will not be affected by the first.
5) I dont think so.
Hope this helps and Best of Luck

Answer 2

for Questions 1-3 try the rhyme
SOH CAH TOA (for Right angled triangles)
SIN = Opposite/Hypotenuse
COS = Adjacent/Hypotenuse
TAN = Opposite/Adjacent

Drawing diagrams will help you determine which is Opposite, Adjacent and Hypotenuse to the angle you are trying to find.

Q4. (From ref 1. below)
An event A' is a complementary event to the event A, if the event A doesn't occur. So, shooting hit and miss are complementary events.

Events A and B are called mutually exclusive ( А В = ), if their simultaneous occurrence is impossible. For instance, an occurrence both heads and tails at throwing of a coin.

Q5. To calculate natural log, use the following approximation[ref 2]

It is well known to mathematicians that a natural log can be calculated to any degree of accuracy, since it is known that the following is true:
ln(1+x)=x-x2/2+x3/3-x4/4+...
The problem is that this is only true for -1 < x < 1.
To use this approximation, you also have to recall that for any number y:
y-1 = 1/y.
Which can be extended to show that:
-ln(y)=ln(1/y)
So, an example would look like this. Suppose we want to find the natural log of 7. You can't plug x=7 into the formula, since x has to be between -1 and 1. But, you do know that if you can find the log of 1/7, then the log of 7 is the negative of that. To find, the log of 1/7, you set x = -6/7. Then, an approximation using only the first term is:
ln(1/7)=ln[1-(6/7)]=(-6/7)=-.857
As you continue to calculate more terms, the approximation will get better and better. Including the second term gets you:
ln(1/7)=ln[1-(6/7)]=(-6/7)-(-6/7)2/2=-.857-.367=-1.224
The third term is (-6/7)3/3, which equals -.210, pushing the approximation ot -1.425 and so on.

Answer 3

1. visualise a right angled triangle and pick an angle in the triangle you want to find. the side that is not touching that angle will be opposite, the touching that makes a 90 degree (right angle) with the opposite will be adjacent...
try to remember when to use the sine/cosine/tangent by using SOC CAH TOA...if that doesn't help use: sino (o represents opposite over hypotenuse), cosa (adjacent over hypotenuse) and tan (last one, so it can only be opposite over adjacent!)...remember, you can never have hypotenuse over adjacent/opposite, as that will give you more than 1 and that will NOT work on your calculator...plus REMEMBER to set your calculator at DEGREE mode, NOT radian...i've heard of many screw ups all because of the mode...

2. sine rule is applied when you know size of an angle and the size of the opposite side to that angle and is given either the size of another angle within an odd triangle and is asked to find the length of the side opposite to that angle, or, when you are given the size of another side of the same triangle and are asked for the size of the angle opposite of that side. you always put what you are looking for as the neumerator, hence if you are looking for the size of the angle, then you use "sinA/a = sinB/b"
Cosine rule is used when you know the size of the angle and the length of the two sides that are adjacent to the angle and are asked the length of the third side opposite to the given angle or you are given length of all 3 sides and are asked to find one of the angles.

3. well, my mom told me u can use some table method, but i'm sure that they would let u use ur calculator for doing sines and cosines and tangents.

4. complementary of an event (e.g. A) means an event that excludes the complemtary of (e.g. A)...often noted as P(A') if it is a complement of A. mutually exclusive events are when 2 events will not occur together.

5.you can work out the log of a number without a calculator if it is an easy one...all u need to do is think really...i'm a freshman i this.

good luck!

Answer 4

1) Find the hypotenuse(longest).. this is n't it. Look at the angle you are using/finding..the side OPPOSITE that is the opposite.
You've only one left now...the adjacent.
2) Sine and cosine rule when you don't have a right angled triangle. When you know lots of angles...sine rule...when you know lots of sides...cos rule.Don't panic if you can' remember this,try one,if it does n't work just try the other,you'll find out in a few seconds.
3) Only by using log tables...have you got a log book?
4) If A AND B can happen...multiply
If only A OR B can happen....add.
5) Again only if you have log tables...these are what we had to use to do our A levels in the 70s.get some they're easy once you learn how.Hope I was in time.

Answer 5

1) First off, SOHCAHTOA *only* applies to right angle triangles. After choosing an angle, the opposite is the side which the angle projects on, the hypotenuse is ALWAYS the longest side (opposite to the 90 degree angle), and the adjacent is the remaining side.

2) The sine and cosine rules apply to ALL triangles (not just right angle ones). You apply the cosine rule when you're given all sides but no angles, and the sine rule at all other times.

Answer 6

For Q's 1,2,4 agree broadly with other respondents.
For 3 either construct rt- angled triangle and use SOHCAHTOA *to determine the ratios of the sides using scale drawing and protractor or the mclaurin expansion for the particular trig function,if you're keen and dedicated and can't use a calculator.
For 5 just remember that the log of any number in a given base is the power to which that base is raised to eqal that number!?
OK example log(base10)100 =2 'cause 10^2= 100
or log(base10) 1million= 6 'cause 10^6= 1million
Also remember logs being exponents are additive (10^3*10^2=10^5), so if log5=0.699, then it follows log2=0.301,
since 5*2= 10 and log 10 by defn=1. I do NOT think you will be asked to calculate the logs of 'difficult' numbers manually, merely to demonstrate a knowledge of their meaning and properties
*SOHCAHTOAH famous mathematician's island which exploded catstrophically after Godel published his famous theorem!

Answer 7

1. Oliver Horse Ate Heaps Of Apples.
Sin: opp/hyp
Cos: adj./hyp
Tan: opp./adj.

2. Use the cosine rule when you only have one Angle, sine rule when you have only two sides and two angles.

3. Only perfect sines and cosines, like 45, 60, 90 degrees..etc. Use a scientific calc.

4. Mut. Exclu. is where both events can't happen. Comp. is where one must happen but both can't. Sounds the same but they're not. Mut. excl. is Prob = A+B, where Compl. is P=1-P(B)

5. Natural or base 10? If it's natural just take the exponential of both sides...exp(x)=exp(ln(x))...the exp(Ln(x)) is just x. Your final would be exp(x)=x.

Base 10...Example: log(x)=4 is your equation, so what's x?, just do this: 10^log(x)=10^4, this is the same as x=10^4. so x=10000.

Answer 8

Try not to panic. The test is going to measure your ability in all sorts of areas so it's hard to revise for. The revision you've been doing over the past ten years is what they're after! :-)

1. Sine/cosine/tangent: memorise the Japanese-sounding phrase, soh cah toa (where sine = opposite divided by hypotenuse.....the side opposite the angle is the opposite......cah: cosine = adjacent divided by hypotenuse and so on for tangent).

2. http://www.ucl.ac.uk/Mathematics/geomath/trignb/trig11.html

3. Try google/wikipedia

4. http://www.peterwebb.co.uk/probability.htm
Scroll down to "THE LAYMAN'S GUIDE TO PROBABILITY THEORY"

5. http://www.sosmath.com/algebra/logs/log4/log44/log44.html

Answer 9

I feel that you are clutching at straws in asking so many theoretical questions rather than specific questions.
It is difficult to give theory on a site such as this whereas specific questions could be addressed.
Your best bet would be to sit down with a maths person who,with the aid of pencil and paper could address the topics you raise.

Answer 10

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