Question

sec(theta/4)=sqrt2

Answer 1

\[\sec (\frac{ \Theta }{ 4 })=\sqrt{2}\]

Answer 2

@Miracrown

Answer 3

Use the relation sec(x) = 1/cos(x).

Answer 4

can you show me how to do it please

Answer 5

hello? @shiraz14

Answer 6

Let x=θ/4. Then we have:

sec(θ/4) = 1/[cos(θ/4)] = √2
=> cos(θ/4) = 1/(√2)

Now, consider the following diagram:



This is a special isosceles triangle where θ/4 = 45 deg => θ=180 deg
So the general solution of θ is θ=180+2n(360) deg. or θ=(π+2nπ) rads.

Answer 7

so whats the answer pi+2npi?

Answer 8

@brucek69 : Yes, that's correct (if you want the answer in radians). I should modify the triangle a little as follows: