Question

On a unit circle, the terminal point of Theta is

(Sqrt2/2, sqrt2/2). What is theta
A.
Pi/6
B.
Pi/3
C.
Pi/4
D.
Pi/2

Answer 1

C.
`(\pi)/(4)`

Explanation:

`terminal \: point \: of \: \theta = \bigg( ( √(2) )/(2), \: \: ( √(2) )/(2) \bigg) \\ \\ \implies \: (x, \: \: y) = \bigg( ( √(2) )/(2) \: \: ( √(2) )/(2) \bigg) \\ \\ \implies \: x = ( √(2) )/(2), \: \: y = ( √(2) )/(2) \\ \\ \because \tan \theta = (y)/(x) \\ \\ \therefore \tan \theta = ( ( √(2) )/(2) )/( ( √(2) )/(2) ) \\ \\\therefore \tan \theta =1 \\ \\ \implies \tan \theta =\tan \bigg( (\pi)/(4) \bigg) \\ \\ \implies \: \theta \: = (\pi)/(4)`