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How do I solve the equation the equation sin(theta) - cos(theta) = sqrt( 2 ) ?
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= .
Multiply both sides by . You will get
= 1. (1)
Notice and use that = = .
Then from (*) you will get
= 1. (2)
Now use the formula sin(a)*cos(b) - cos(a)*sin(b) = sin(a-b). Then from (2) you will get
= 1.
It implies
= .
Then = = .
It is the same as = in the interval 0 <= < .
The plot below confirms the solution ( ~= 2.33 )
Plots y = and y =
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There is a bunch of my lessons on solving trig equations in this site
- Solving simple problems on trigonometric equations
- Solving typical problems on trigonometric equations
- Solving more complicated problems on trigonometric equations
- Solving advanced problems on trigonometric equations
- OVERVIEW of lessons on calculating trig functions and solving trig equations