Incorporate the use of the double angle formulas identities and other identities to solve for the following on

My Attempt:

0 and 180 and 360

Textbook Answers:

0 and 45 and 135 and 180 and 225 and 315 and 360

What am I doing wrong?

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- Nov 21st 2007, 07:11 PMMacleefSolving Trig Equations
Incorporate the use of the double angle formulas identities and other identities to solve for the following on

My Attempt:

0 and 180 and 360

Textbook Answers:

0 and 45 and 135 and 180 and 225 and 315 and 360

What am I doing wrong? - Nov 21st 2007, 08:08 PMSoroban
Hello, Macleef!

A silly mistake . . . don't kick yourself too hard.

Quote:

Solve for

My Attempt:

. . . . no

We have: .

. .

Factor: .

Then: .

And: .

. . . .

- Nov 21st 2007, 08:18 PMticbol
What did you do wrong?

From sinX /cosX = 2sinXcosX, how did you get sinX = 2sinX? What happened to the two cosX's?

You want me to solve the Problem?

After your sinX/cosX = 2sinXcosX,

Bring them all to the lefthand side,

sinX/cosX -2sinXcosX = 0

sinX(1/cosX -2cosX) = 0

sinX = 0

X = arcsin(0) = 0, 180, 360 degrees ---------***

1/cosX -2cosX = 0

Clear the fraction, multiply both sides by cosX,

1 -2cos^2(X) = 0

1 = 2cos^2(X)

1/2 = cos^2(X)

cosX = +,-sqrt(1/2)

cosX = +,-1/sqrt(2)

X = arccos(+,-1/sqrt(2))

X = 45, 135, 225, 315 degrees. ------***

Therefore, X = 0, 45, 135, 180, 225, 315, 360 degrees.