Theorem 3

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General solution of tan q = k

Let a be the least positive angle, such that tan a = k.

tan q = tan a.

Also tan (p + a ) = tan a = k.

q = a or p + a = any other co-terminal angle

q = a, 2p + a, 4p + a, ....., p + 2p + (p + a) ....

General solution is q = np + a.

Particular Cases

\q = np + a = np+ 0

Example:

Solve the following trigonometrical equations lying between 0 and 2p.

Suggested answer:

sin 2q is positive in I and II quadrants.

cos 2q is positive in I and IV quadrants.

Let 2q = a.