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MissTica
3 years ago
12

If sinA =3/5 and A+B =90 find cosB

Mathematics
1 answer:
-Dominant- [34]3 years ago
8 0

A+B=90^o\to B=90^o-A\\\\\cos B=\cos(90^o-A)=\cos90^o\cos A+\sin90^o\sin A\\\\=\cos A+1\cdot\dfrac{3}{5}=0+\dfrac{3}{5}=\dfrac{3}{5}\\\\\boxed{\cos B=\dfrac{3}{5}}

Used:\\\\\cos(x+y)=\cos x\cos y+\sin x\sin y\\\\\cos90^o=0,\ sin90^o=1

Other method:

Look at the picture.

\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\sin A=\dfrac{3}{5}\to opposite=3\ and\ hypotenuse=5

\cos\theta=\dfrac{adjacent}{hypotenuse}\\\\adjacent=3\ and\ hypotenuse=5\to\cos B=\dfrac{3}{5}

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