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Prelim 2016 Maths Help Thread (1 Viewer)

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eyeseeyou

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Find in the simplest surd form the value of:

a. tan15
b.cos15
 

eyeseeyou

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If sin (theta)=3/4, 90 degrees is smaller than (theta) is smaller than 180 degrees, evaluate in surd form,

a. Sin2(theta)
b. cos2(theta)
c.tan2(theta)
In which quadrant does 2(theta) lie in?
 

eyeseeyou

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1.Use expansion of sin(A+B) to evaluate sin 195
2.Simplify 1/2sin(theta)tan(theta)
 

eyeseeyou

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I can't seem to work these easy questions out for some reason although I can work out others
 

Drongoski

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Find in the simplest surd form the value of:

a. tan15
b.cos15
Let T stand for tan 15

tan 30 = tan (15+15) = 2T/(1-T^2) = 1/sqrt(3)



Choose the positive value.

i.e. tan 15 = 2 - sqrt(3)


For cos 15, again use a double angle formula:

2 cos215 = 1 + cos (15+15) = 1 + sqrt(3)/2
 
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eyeseeyou

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I do not know what I am doing wrong for the following questions:

a. sin4xcos4x
b. 1+cos(180+2(theta))
c.sinxcosxcos2x
d. 2sin2xcos2x
 

eyeseeyou

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I tried it and ended up with all these weird values

iirc you have to use double andgle formula for these q's
 

eyeseeyou

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Let T stand for tan 15

tan 30 = tan (15+15) = 2T/(1-T^2) = 1/sqrt(3)



Choose the positive value.

This cannot be right??
I used tan (45-30) and ended up getting -1/3 (I am sure this answer isn't right)
 

InteGrand

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I used tan (45-30) and ended up getting -1/3 (I am sure this answer isn't right)




(LaTeX may take a while to load, it seems to have been that way on this site today. Basically, using that method you should get (√(3) – 1)/(√(3) + 1). How did you end up with -1/3?)

This can be simplified to 2 – √(3) by rationalising the denominator.
 
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eyeseeyou

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(LaTeX seems to be taking a while to load. Basically, using that method you should get (√(3) – 1)/(√(3) + 1). How did you end up with -1/3?)
You were supposed to use the tan rule for this question iirc
 

eyeseeyou

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(LaTeX may take a while to load, it seems to have been that way on this site today. Basically, using that method you should get (√(3) – 1)/(√(3) + 1). How did you end up with -1/3?)
The answer is actually 2-Sqaureroot of 3
 

eyeseeyou

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(2tantheta)/(1-tan squared theta) when theta = 22.5 degrees

sin squared 50+sin squared 40
 

InteGrand

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1.Use expansion of sin(A+B) to evaluate sin 195
2.Simplify 1/2sin(theta)tan(theta)
1) Do sin(195°) = sin(135° + 60°), for example, since we know the values of trig. functions at 135° and 60°.
 

eyeseeyou

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If sin (theta)=3/4, 90 degrees is smaller than (theta) is smaller than 180 degrees, evaluate in surd form,

a. Sin2(theta)
b. cos2(theta)
c.tan2(theta)
In which quadrant does 2(theta) lie in?
1.Use expansion of sin(A+B) to evaluate sin 195
2.Simplify 1/2sin(theta)tan(theta)
Did someone forget these 2?
 
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