In right triangle ABC, sin A = 2/5. Find sin(90degrees - A) Please explain?

1 Answer
Jim G.
Apr 1, 2018

#+-sqrt21/5#

Explanation:

#" using the following "color(blue)"trigonometric identities"#

#•color(white)(x)sin(90-x)^@=cosx^@#

#•color(white)(x)sin^2x+cos^2x=1#

#rArrcosx=+-sqrt(1-sin^2x)#

#rArrsin(90-A)=cosA#

#cosA=+-sqrt(1-(2/5)^2)#

#color(white)(cosA)=+-sqrt(1-4/25)=+-sqrt(21/25)#

#rArrsin(90-A)=cosA=+-sqrt21/5#

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