Rewrite in the form indicated and hence solve for x (in radians to 2dp) in the interval [0, 2π]: (a) 4sinx- 3cosx= 2.5 Rsin(x-a)
(b) 5cos+ 12sin=6 Rsin(x+a)
(c) cos(x) +sin(x) =1/2 Rsin(x+a)
Thankyouuu! 
+128707 I'm not sure this is what is being asked......but I'll take a plunge...
a) Here's a graph of the first thing, y = 4sinx - 3cosx..........https://www.desmos.com/calculator/jj8zbyumyb
This looks like a normal sine graph shifted to the right by about .644 rads with an amplitude of 5....
Thus, we have ... 2.5Rsin(x-a) = 5sin(x - .644)......so "R" = 2 and "a" = .644
b) Here's the graph of 5cosx + 12sinx .......... https://www.desmos.com/calculator/twnz1jzolm
This looks like the normal sine graph shifted to the left by about 1.18 rads with an amplitude of 13
Thus, we have......6Rsin(x + a) = 13sin(x + 1.18).......so "R" = (13/6) and "a" = 1.18
c) Here's the graph of cos(x) + sin(x).........https://www.desmos.com/calculator/ogzlnnpzih
This looks like the normal sine graph shifted to the left by pi/4 rads with an amplitude of √2
Thus, we have....... (1/2)Rsin(x + a) = √2sin(x + pi/4)......so "R" = 2√2 and "a" = pi/4
I hope this is what was intended !!!
+128707 I'm not sure this is what is being asked......but I'll take a plunge...
a) Here's a graph of the first thing, y = 4sinx - 3cosx..........https://www.desmos.com/calculator/jj8zbyumyb
This looks like a normal sine graph shifted to the right by about .644 rads with an amplitude of 5....
Thus, we have ... 2.5Rsin(x-a) = 5sin(x - .644)......so "R" = 2 and "a" = .644
b) Here's the graph of 5cosx + 12sinx .......... https://www.desmos.com/calculator/twnz1jzolm
This looks like the normal sine graph shifted to the left by about 1.18 rads with an amplitude of 13
Thus, we have......6Rsin(x + a) = 13sin(x + 1.18).......so "R" = (13/6) and "a" = 1.18
c) Here's the graph of cos(x) + sin(x).........https://www.desmos.com/calculator/ogzlnnpzih
This looks like the normal sine graph shifted to the left by pi/4 rads with an amplitude of √2
Thus, we have....... (1/2)Rsin(x + a) = √2sin(x + pi/4)......so "R" = 2√2 and "a" = pi/4
I hope this is what was intended !!!
