# trig

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Solve tan2A - 2tanA = -1 for 0º≤A≤360º.

• trig -

Hmmm. Sensing a missing ^ character, we have

tan^2(A) - 2tanA + 1 = 0
(tanA - 1)^2 = 0
tanA = 1
So, A = 45º or 225º

• trig -

or taking it at face value the way it was typed

tan 2A - 2tan A = -1
2tanA/(1-tan^2 A) - 2tanA = -1
let tanA = x for easier typing

2x/(1-x^2) - 2x = -1
times 1 - x^2

2x - 2x + 2x^3 = -1 + x^2
2x^3 - x^2 + 1 = 0
by Wolfram
http://www.wolframalpha.com/input/?i=2x%5E3+-+x%5E2%2B1%3D0
x = -.657298
tanA = -.657298
A = 146.7° or A = 326.7°

both work

• trig -

a ladder leaning against a vertical wall make an angle 24 degrees with the wall.the foot of the ladder is 5 ft from the wall find the length of the ladder

• trig -

You lean a ladder 6.7 m long against a wall. It makes an angle of 63 degrees with the level ground. How high up is the top of the ladder?

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