Question

If sin x = .21,what is cos x?

Answer 1

Use this : \[\sin^2x + \cos^2x = 1\]

Answer 2

Or in simpler way :
\[cosx = \sqrt{(1 - \sin^2x)}\]

Answer 3

Because there are two values of x will give you a value of 0.21 there will be two solutions to this question. To find the first value we can directly solve the angle using:\[\sin x =0.21\]\[ x = \sin^{-1}{(0.21)} \]\[x= 12.1222^o\]
now we can obtain the first solution through direct substitution:
\[\cos x_1 = \cos(12.1222^o)\]
\[\cos x_1 = 0.9777\]

the second angle comes from the cast diagram and utilizes the first angle you solved. the attached picture shows how to solve the second angle that satisfies sinx = 0.21. substitute this angle into cosx to obtain your second solution:
\[\cos x_2 = \cos(167.87^o)\]
\[\cos x_2 = -0.9777\]

As it turns out, theses arre the same solutions you get through @waterineyes 's method when considering that roots usually contain a positive and negative pair