Home > Trigonometry > Trigonometric Functions of Any Angle

How do you evaluate #cos [(pi)/4]#?

Answer 1

#cos (pi/4)=sqrt(2)/2# see explanation for details.

Angle #pi/4# rad or #45^@# can be an angle in isosceles right triangle, so its catheti are equal and its hypothenuse is #sqrt(2)# times longer. For example if the catheti are #1# unit long, then the hypothenuse is #sqrt(2)# units.

Sine is a quotient of the cathetus opposite to the angle and the hypothenuse, so:

#sin 45^@=1/sqrt(2)=sqrt(2)/2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Charles Autterson

To evaluate cos(π/4), you can use the unit circle or trigonometric identities. In this case, since π/4 corresponds to 45 degrees, you can use the fact that cos(45 degrees) equals 1/√2 or √2/2. Therefore, cos(π/4) equals √2/2.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.