IB Maths HL, SL, Studies: January 2014

Wednesday, January 29, 2014

Trigonometry, Trigonometric equations, IB Math HL

IB Mathematics HL – Trigonometry, Trigonometric equations, tanx

How can we solve the following trigonometric equation?

$tan^2x=1$ in the interval $[0,2\pi]$ .

The solution

IB Math HL – Trigonometry, Trigonometric equations

$tan^2x=1 \Rightarrow tanx=1 \ or tanx=-1$

First we’ll solve the trigonometric equation $tanx=1$

$tanx=1 \Rightarrow x=\frac{\pi}{4} \ or x=\pi+\frac{\pi}{4}=\frac{5\pi}{4}$

and then the other trigonometric equation $tanx=-1$ .

$x= \frac{3\pi}{4} \ or x=2\pi-\frac{\pi}{4}=\frac{7\pi}{4}$

Therefore, the solutions are

$x=\frac{\pi}{4} , \frac{5\pi}{4} , \frac{3\pi}{4} , \frac{7\pi}{4}$

Question and answer is here
http://www.ibmaths4u.com/viewtopic.php?f=3&t=438

IB math questions and answers by www.ibmaths4u.com

Tuesday, January 28, 2014

Trigonometry, Trigonometric formulas, IB Math HL

IB Mathematics HL – Trigonometry, Trigonometric identities, double angle formula

How can we simplify the following trigonometric expression?

$\frac{sin4x(1-cos2x)}{cos2x(1-cos4x)}$

Question and answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=439

IB math questions and answers by www.ibmaths4u.com

Tuesday, January 21, 2014

Integration, Integrals - IB Math HL

Integration, Integrals - IB Mathematics HL

How can we find the real number p>1 for which the following definite integral equals to 2?

$\int^p_1(1+\frac{1}{x^2}) \ dx$

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=422

IB math questions and answers from www.ibmaths4u.com

Integration, Definite Integrals - IB Mathematics IB maths SL

Integration, Definite Integrals - IB Mathematics IB maths SL

How can we find the real number a>1 for which the following definite integral equals to 4?

$\int^a_1(1+\frac{1}{x^2}) \ dx$

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=11&t=426

IB maths from www.ibmaths4u.com