Question

If 5sinα=4 then find the value of cos 2α

Answer 1

Answer:

cos 2a = -7/25

magnitude : 7/25

Step-by-step explanation:

given, 5sina = 4

sin a = 4 / 5 (opposite side / hypotenuse)

from Pythagorean theorem,

adjacent side = $\sqrt{(hypotenuse)^2 - (opposite side)^2}$

so, adj side = $\sqrt{5^2 - 4^2}$

==> adj side = $\sqrt{25 - 16}$

==> adj side = $\sqrt{9}$

==> adj side = 3

we know that cos a = adjacent side / hypotenuse

==> cos a = 3 / 5

Now ,

cos 2a = cos^2 a - sin^2 a

cos 2a = ( cos a + sin a )*( cos a - sin a )

cos 2a = ( 3/5 + 4/5 ) * ( 3/5 - 4/5 )

cos 2a = 7/5 * -1/5

cos 2a = -7/25

If considered only magnitude,

cos 2a = 7/25

( And the triangle is in second quadrant)

I hope this answer is helpful :)