Question

"The straight line equation y=(3/4)x makes an acute angle k with the x-axis.

Find the value of sin2k and cos2k"

Answer 1

can u help me plz

Answer 2

I'm sorry, I can't!

Answer 3

why?

Answer 4

Because I don't know how to work it out.

Answer 5

ok thx

Answer 6

in general, for any line the slope equals the tangent
\[\tan (k) = slope = \frac{3}{4}\]
find sin(k), cos(k) using right triangle

notice i solved for hypotenuse using pythagorean thm
now using SOH CAH TOA
\[\sin(k) = \frac{3}{5}\]
\[\cos(k) = \frac{4}{5}\]
double angle identities
\[\sin (2k) = 2\sin k \cos k = 2*\frac{3}{5}*\frac{4}{5} = \frac{24}{25}\]
\[\cos (2k) = \cos^{2} k - \sin^{2} k = (\frac{4}{5})^{2} - (\frac{3}{5})^{2} = \frac{7}{25}\]
there you go, hope that helps