Question

given : sin theta = p/q. Find cos theta + sin theta in terms of p and q

Answer 1

Answer:

Step-by-step explanation:

GIVEN SIN Ф = P/Q

SIN Ф = OPPOSITE SIDE/HYPOTENUSE.

IMPLIES;

OPPOSITE SIDE,O = P

HYPOTENUSE ,H= Q

ADJACENT SIDE ,A= ?

USING PYTHAGORAUS THEOREM,

H² = O²+A²

Q² = P²+A²

A²= Q²-P²

A = √(Q²-P²).

COS Ф = ADJACENT SIDE / HYPOTENUSE

COS Ф = √(Q²-P²)/Q

SIN Ф+ COS Ф= P/Q+√(Q²-P²)/Q

                        =[ P+√(Q²-P²) ] / Q.

HOPE THIS HELPS.