Simple trig maths question (1 Viewer)

[x.Exhaust.x]

1 - 2cos squared theta = 0

The teacher wrote 4 solutions, but I got 3...

Edit: Find the angles.

 

[pLuvia]

1-2cos²@=0
cos@=+1/sqrt{2}
@=pi/4, 3pi/4, 5pi/4, 7pi/4

Use the ASTC method

 

[aidyllic]

what were your answers?

i got @ = 45, 135, 225, 315

1 - 2 cos²@ = 0
- 2cos²@ = -1
cos²@ = 1/2
cos@ = ±1/√2

your answers will also depend on the range. e.g. 0 ≤ @ ≤ 360

hope this helps, i actually have an exam on trig tomorrow so that's what i've been doing..

 

[x.Exhaust.x]

I don't see why it's 225 degrees and 135 degrees. I got 45 degrees and 315 degrees.

In the end I got cos theta as 45 degrees

If you use ASTC it's positive in quadrants 1 and 4. Why is it also in quadrants 2 and 3?

 

[m&ss2008]

If you use ASTC it's positive in quadrants 1 and 4. Why is it also in quadrants 2 and 3?

when you take the square root you have to allow for the plus and minus.

for example.
3^2=9
(-3)^2=9
therefore sqrt9=+-3

same applies for algebra, trigonometry, etc
then with ASTC the positive has two results, the negative has two results
(if 0<@<2pi)