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by **nicole** » Wed Jan 29, 2014 7:25 am

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

by **miranda** » Wed Jan 29, 2014 7:26 am

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!

by **nicole** » Wed Jan 29, 2014 7:26 am

Thank you!!

ib maths4u | ib maths | ib math | ib mathematics

Trigonometry, Trigonometric equations, IB Math HL

Trigonometry, Trigonometric equations, IB Math HL

Trigonometry, Trigonometric equations, IB Math HL

Re: Trigonometry, Trigonometric equations, IB Math HL