If sinA=-3/5 with A in QIII

Question

what is sin A/2 and csc A/2?

Answer 1

The expression and Angle A lies in Quadrant |||.

Let be an angle in standard position with (x, y) a  point on the terminal side of and .

y is negative in Quadrant |||, let .

So,

x is negative in Quadrant |||. So, .

Half angle identities

Therefore,

Comments

The angle A lies in QIII, so .

Therefore the angle A/2 lies in QII. The values of sin and csc functions are positive in QII.

Half angle identities : .

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