Question

(1)
3 sin x + 28 cos x
dx
5 sina 6 cos x​

Answer 1

Answer:

General Solution

Since trigonometrical functions are periodic functions, solutions of trigonometric equations can be generalized with the help of the periodicity of the trigonometrical functions. The solution consisting of all possible solutions of a trigonometric equation is called its general solution.

We use the following formulae for solving the trigonometric equations:

· sin q = 0 Þ q = np,

· cos q = 0 Þq = (2n + 1),

· tan q = 0 Þ q = np,

· sin q = sin a Þq = np + (–1)na, where aÎ [–p/2, p/2]

· cos q = cos aÞq = 2np ± a, where aÎ [ 0, p]

· tan q = tan a Þ q = np + a, where aÎ ( –p/2, p/2)

· sin2 q = sin2 a , cos2 q = cos2 a, tan2q = tan2 aÞq = np±a,

· sin q = 1 Þq = (4n + 1),

· cos q = 1 Þ q = 2np ,

· cos q = –1 Þ q = (2n + 1)p,

· sin q = sin a and cos q = cos aÞ q = 2np + a.