Take Note Properties: Cofunction Identities

Problem 1 Verifying an Angle Identity

Verify the identity sin ( θ − π 2 ) = − cos θ . sine . open . theta minus , pi over 2 . close . equals negative cosine theta . .

sin ( θ − π 2 ) = sin ( − ( π 2 − θ ) ) b − a = − ( a − b )   = − sin ( π 2 − θ ) sin ( − θ ) = − sin θ   = − cos θ sin ( π 2 − θ ) = cos θ table with 3 rows and 3 columns , row1 column 1 , sine . open . theta minus , pi over 2 . close , column 2 equals sine . open . negative . open . pi over 2 , minus theta . close . close , column 3 b minus eh equals negative . open , eh minus b , close , row2 column 1 , , column 2 equals negative sine . open . pi over 2 , minus theta . close , column 3 sine . open , negative theta , close . equals negative sine theta , row3 column 1 , , column 2 equals negative cosine theta , column 3 sine . open . pi over 2 , minus theta . close . equals cosine theta , end table

✓ Got It?

1. Verify the identity cos ( θ − π 2 ) = sin θ . cosine . open . theta minus , pi over 2 . close . equals sine theta . .