Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. cot(u) = −2, 3𝜋/2 < u < 2𝜋

Answer 1

cot u = -2, tan u = ?

sin u = ?

cos u = ?

Now uses double and formulas

Answer 2

cot(u) =-2 = base/height = -2/1= 2/-1, base=2, height =-1

tan(u) = 1/cot(u) = -1/2

u is in the 4th quadrant where sin(u)<0, tan(u)<0 and cos(u)>0.

3pi/2<u<2pi is the 4th quadrant

construct a right triangle with base =2, height =-1,

use the Pythagorean theorem to solve for the hypotenuse =sqr5

hypotenuse = square root of (2^2 + (-1)^2) = sqr(4+1) = sqr5

sin(u) =height/hypotenuse = -1/sqr5

cos(u) =base/hypotenuse = 2/sqr5

use the double angle formulas:

sin(2u) = 2sin(u)cos(u) = (-1/sqr5)(2/sqr5) = -4/5

cos(2u) = cos^2(u)-sin^2(u) = (2/sqr5)^2 - (-1/sqr5)^2 = 4/5 -1/5= 3/5

tan(2u) = 2tan(u)/(1-tan^2(u)) = 2(-1/2)/(1-1/4) = -1/(3/4) =-4/3

or tan(2u) = sin(2u)/cos(2u) = (-4/5)/(3/5) = -4/3