Question

What is cos 0 when sin 0 =2/5

Answer 1

Step by step Step-by-step explanation :

We know,

sin θ =
`\:\mathsf{(opposite)/(hypotenuse)}`

here,

sin 0 =
`\:\mathsf{(2)/(5)}`

So,

opposite must be 2

and hypotenuse will be 5

Now,

By Pythagoras theorem

Adjacent =
`\:\mathsf{\sqrt(hypotenuse²)-(opposite²)}`

=> Adjacent =
`\:\mathsf{\sqrt(5²)-(2²)}`

=> Adjacent =
`\:\mathsf{\sqrt(25)-(4)}`

=> Adjacent =
`\:\mathsf{\sqrt(21)}`

Now as adjacent =
`\:\mathsf{\sqrt(21)}`

We know,

cos θ =
`\:\mathsf{(Adjacent)/(hypotenuse)}`

=> cos θ =
`\:\bf\boxed{(√21)/(5)}`

Hope this helps you!

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The calculation is lengthy but if you know the concept then it's very easy

I would suggest you to learn all the trigonometric ratios and these trigonometric functions.

Thank you!