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