How do you evaluate $cos(sin^-1(-1/4))$ without a calculator?

Question

11509 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-29T07:09:43

$=sqrt 15/4$

Let $a=sin^(-1)(-1/4) in Q4$ , wherein cosine is positive.

The given expression is

$cos a$

$=sqrt(1-sin^2 a)$

$=sqrt(1-(-1/4)^2)$

$=sqrt 15/4$ .

Instead of the principal a or any other value in Q4, if we choose a

value in Q3, wherein cosine is also negative, the answer will be #-

sqrt 15/4#

For $sin a = -1/4$ , the principal a in Q4 is -13.4775^o#, nearly.

An a in Q3 is $194.4775$ , nearlr, and for this a,

$sin a =-1/4 and cos a =-sqrt 15/4$ .

Yet, according to the convention for the choice of a as the principal

value, the sign is positive...

-

How do you evaluate cos(sin^-1(-1/4))cos(sin^-1(-1/4)) without a calculator?