How do you simplify #cos^-1(sqrt2/2)#?

2 Answers
Aug 3, 2017

#cos^-1(sqrt2/2)=pi/4#

Explanation:

This value is actually a standard value in disguise. Surds are often removed from the denominator of a fraction by multiplying top and bottom by the surd in question. We can do exactly the same thing to put the surd back in the denominator:

#sqrt2/2*sqrt2/sqrt2=2/(2sqrt2)=1/sqrt2#

Maybe you recognise the value now.

What value of theta gives this value? It is one that should be memorised if you have exams on trigonometry.

#cos^-1(sqrt2/2)=cos^-1(1/sqrt2)=pi/4#

Writing this another way, we have:

#cos(theta)=sqrt2/2=1/sqrt2#

#theta=pi/4#

Aug 3, 2017

#pi/4; (7pi)/4#

Explanation:

Trig table and unit circle give -->
#cos x = sqrt2/2# --> arc #x = +- pi/4#,
or, using co-terminal arcs:
#x = pi/4# and #x = (7pi)/4#