trigonometric graph

**zuuberbat** · November 11th 2008, 08:32 PM

Prof never went over this in class, don't really know what to do..

Find the first three x-intercepts of the graph of the given function on the positive x-axis.

f(x) = 1 - 2cos(x+pi/3)

Any help (explanations, steps) would be great, thanks!

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Also... have a problem with this question..

Use the given information to find the values of the remaining five trigonometric functions.

cotx = 1/2, pi < x < 3pi/2

Thanks ><!

**mr fantastic** · November 11th 2008, 11:23 PM

Originally Posted by zuuberbat

Prof never went over this in class, don't really know what to do..

Find the first three x-intercepts of the graph of the given function on the positive x-axis.

f(x) = 1 - 2cos(x+pi/3)

[snip]

Solve $1 - 2 \cos \left( x +\frac{\pi}{3} \right) = 0 \Rightarrow \cos \left( x + \frac{\pi}{3} \right) = \frac{1}{2}$ for x > 0.

**mr fantastic** · November 11th 2008, 11:27 PM

Originally Posted by zuuberbat

Prof never went over this in class, don't really know what to do..

Find the first three x-intercepts of the graph of the given function on the positive x-axis.

f(x) = 1 - 2cos(x+pi/3)

Any help (explanations, steps) would be great, thanks!

------------------------------------------------------

Also... have a problem with this question..

Use the given information to find the values of the remaining five trigonometric functions.

cotx = 1/2, pi < x < 3pi/2

Thanks ><!

Obviously tan x = 2.

Substitute into $\sin^2 x + \cos^2 x = 1 \Rightarrow \tan^2 x + 1 = \frac{1}{\cos^2 x}$ and solve for $\cos x$ (note that $\cos x < 0$ for $\pi < x < \frac{3 \pi}{2}$ )

Get sin x from cos x etc.

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