SOLUTION: Solving Trig Equations What do I do if my trig equation does not equal a reference triangle? example: sec 2 theta = 1 I know that sec=Hypotenuse/adjacent, but how do I graph a

Question 797441: Solving Trig Equations
What do I do if my trig equation does not equal a reference triangle?
example:
sec 2 theta = 1
I know that sec=Hypotenuse/adjacent, but how do I graph a triangle with a hypotenuse of 1 and an adjacent angle of 1? I am familiar with graphing points on a plane (ex: cos theta = 1, graph at point (1,0)) but 1) I am using secant, the opposite of cosine, and 2) I am working with secant 2 theta, not just 1 theta.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If sec(2 theta) = 1,
cos(2 theta) = 1
------
2 theta = 0 degrees or 360 degrees
------
theta = 0 degrees or 180 degrees
=================================
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Cosine is NOT the opposite of secant. That would mean that FALSE! Cosine is the reciprocal of secant. .

So: . But since .

Now you need the double angle formula for cosine: . So:

But since :

A little algebra music, Sammy

or

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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