# Trig Help Please

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• Jul 16th 2007, 11:02 AM
janvdl
Trig Help Please
This is something I've never really gotten the hang of...

If tan 20 = t ; how could the following be expressed in terms of t?

a) tan 70
b) tan 40
c) tan 200
d) sec 20

My answers:

a) $\displaystyle \frac{1}{t}$

b) $\displaystyle ?$

c) $\displaystyle t$

d) $\displaystyle \sqrt{(t^2 + 1)}$
• Jul 16th 2007, 11:33 AM
red_dog
b) $\displaystyle \tan 2x=\frac{2\tan x}{1-\tan ^2x}$

$\displaystyle \tan 40=\frac{2\tan 20}{1-\tan ^220}=\frac{2t}{1-t^2}$
• Jul 16th 2007, 03:05 PM
Soroban
Hello, janvdl!

It looks like you've got the hang of it . . .

Quote:

If $\displaystyle \tan 20 = t$, how could the following be expressed in terms of $\displaystyle t$?

$\displaystyle a)\;\tan 70\qquad b)\;\tan 40\qquad c)\;\tan 200\qquad d)\;\sec 20$

My answers:

$\displaystyle a)\; \frac{1}{t}\qquad b)\;? \qquad c)\;t \qquad d)\;\sqrt{t^2 + 1}$

For (b), use the Double-Angle Identity: .$\displaystyle \tan2\theta \:=\:\frac{2\tan\theta}{1 - \tan^2\theta}$

And your answers are correct . . . nice work!