Trigonometry, Trigonometric equations, IB Math HL

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

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 $[0,2\pi]$.

Thanks
nicole

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm

Trigonometry, Trigonometric equations, IB Math HL

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

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

Hope these help!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

Re: Trigonometry, Trigonometric equations, IB Math HL

Thank you!!
nicole

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm