C2 Trig

Will rep anyone who answers and clearly shows the method for the following:

13) Find the coordinates of the point where the graph of y=2sin(2x+5/6pi) crosses the y axis.

16) Find, to the nearest integer, the values of x in the interval 0 < or equal to x < 180degrees for which 3sin^23x - 7cos3x - 5 = 0.

17) Find, in degrees, the values of theta in the interval 0 < or equal to theta < 360degrees for which 2cos^2theta - costheta - 1 = sin^2theta
Give your answers to 1 decimal place, where appropriate.

Thanks in advance for all your help

Regards, Asad

Reply 1

yusufu

13) set x = 0, and find the corresponding value for y

16 and 17)
use the identity cos^2 x + sin^2 x = 1 to obtain quadratics in cosx. solve for x.

Reply 2

*bobo*

13) x=0
so y= 2sin(5/6pi)
y/2=sin(5/6pi)
y/2=sin150

Reply 3

asadtamimi

thanks bobo, and undry i tried doing what you said but i still cant get anywhere

Reply 4

yusufu

asadtamimi

Will rep anyone who answers and clearly shows the method for the following:

13) Find the coordinates of the point where the graph of y=2sin(2x+5/6pi) crosses the y axis.

16) Find, to the nearest integer, the values of x in the interval 0 < or equal to x < 180degrees for which 3sin^23x - 7cos3x - 5 = 0.

3sin^23x - 7cos3x - 5 = 0
3(1-cos^2 3x ) - 7cos 3x - 5 = 0
3-3cos^2 3x - 7cos 3x - 5 = 0
3cos^2 3x +7cos 3x + 2 = 0
cos3x = 1/6 (-7 +-rt(25)) = -2 or -1/6
-2 is not possible
x = 1/3arccos(-1/6)

similar for 17

Reply 5

*bobo*