Use the double angle identities to find sin2x if sinx= 1/square of 17 and cosx<0 . Give exact answer.

Answer 1

Note: if sin(x)>0 and cos(x)<0, the angle x is in the second quadrant.

therefore
cos(x)=-sqrt(1-sin²(x))

Calculate sin(2x) from the double angle formula:
sin(2x)=2sin(x)cos(x)

Since 2x lies in the third or fourth quadrant, sin(2x) is expected to be negative.

Answer 2

since sine is positive and cosine is negative , x must be in quadrant II

make a diagram in the second quadrant with opposite as 1 and hypotenuse as 17, so the adjacent is 4 by Pythagoras, and
cos x = -4/√17

sin 2x = 2sinxcosx = 2(1/√17)(-4/√17) = -8/17

Answer 3

In a triagle abc angle b is 3 times angle a and angle c is 19 less than 6 times angle a.
What is the size of number a,b, and c