## 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

How can we solve the following trigonometric equation?

$cos4x=-cosx$ in the interval $[0,\pi]$.

Thanks
nicole

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

### Re: Trigonometry, Trigonometric equations, IB Math HL

IB Math HL – Trigonometry, Trigonometric equations

$cos4x=-cosx \Rightarrow cos4x=cos(\pi-x) \Rightarrow$

From unit circle we have the following:

$4x= \pi-x \Rightarrow 5x=\pi \Rightarrow x=\frac{\pi}{5}$ accepted

or $4x=- (\pi-x) \Rightarrow 3x=-\pi \Rightarrow x=-\frac{\pi}{3}$ rejected

or $4x= 2\pi –(\pi-x) \Rightarrow 3x=\pi \Rightarrow x=\frac{\pi}{3}$ accepted

or $4x= 2\pi+\pi-x \Rightarrow 5x=3\pi \Rightarrow x=\frac{3\pi}{5}$ accepted

or $4x= 4\pi –(\pi-x) \Rightarrow 3x=3\pi \Rightarrow x=\pi$ accepted

or $4x= 4\pi+\pi-x \Rightarrow 5x=5\pi \Rightarrow x=\pi$ accepted

or $4x= 6\pi –(\pi-x) \Rightarrow 3x=5\pi \Rightarrow x=\frac{5\pi}{3}$ rejected

Therefore, the solutions are

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