SOLUTION: Sin A = {{{ sqrt (5) / 3 }}} and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A
Algebra ->
Trigonometry-basics
-> SOLUTION: Sin A = {{{ sqrt (5) / 3 }}} and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A
Log On
Question 924283: Sin A = and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Sin A = and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A
***
use x for A
sinx=√5/3
cosx=√(1-sin^2(x))=√(1-5/9)=√(4/9)=2/3
sin(2x)=2sinxcosx=2*√5/3*2/3=4√5/9
cos 2x=cos^2(x)-sin^2(x)=4/9-5/9=-1/9
..
check:
sinx=√5/3
x=48.19
2x=96.38˚
..
sin(2x)≈sin(96.38)≈0.9938 (from calculator)
exact value as computed=4√5/9≈0.9938
..
cos(2x)=cos(96.38)≈-0.1111(from calculator)
exact value as computed=-1/9≈-0.1111
(