(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) x \(\geq\) 360\(^o\) x 0\(^o\) 60\(^0\) 120\(^o\) 180\(^o\) 240\(^o...

Answer Details

a) To complete the table of values for y = 2 cos x + 3 sin x, we need to substitute the given x values into the equation and solve for y. Here are the complete values:

b) To draw the graph of y = 2 cos x + 3 sin x, we can start by plotting the points from the table of values onto the x-y plane. Then, we can connect the points to form the graph of the equation.

c) (i) To solve 2 cos x + 3 sin x = -1, we can use the inverse trigonometric functions to find the angle x that satisfies this equation. For example, we can use the identity cos^2 x + sin^2 x = 1 to solve for either cos x or sin x in terms of the other, then use the inverse cosine or sine function to find the angle x.

(ii) To find the value of y when x = 342°, we substitute this value of x into the equation y = 2 cos x + 3 sin x and solve for y. For example, using a calculator, we can find that y = 2 cos 342° + 3 sin 342° = 1.6.