maths trig solutions

Question

Find all the solutions between −2π and 2π of the equation
cos θ = −1/√2

Answer 1

Unfortunately, the problem is MISWRITTEN.  The use of small n appears to be wrong; it probably meant "pi", i.e. solutions θ are sought in the interval [-two pi, 2 pi].  The attempt to use the Greek letter pi misfired, giving n instead of "pi".

 

There are FOUR solutions: three fourths of pi and five fourths of pi, each with plus or minus affixed!

Answer 2

Cos θ = -1/√2 is the same as cos θ = -√2/2, when you rationalize the fraction.

 

If you're familiar the unit circle, cos θ = √2/2 should be one you remember as cos θ = √2/2, when θ = π/4 and θ = 7π/4

Also, cos θ = -√2/2, when θ = 3π/4 and θ = 5π/4

 

The solutions above in bold are between -2π and 2π