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Geometrical Representation of Conjugate of a Complex Number

,xin quadrant...

Question

, x in quadrant III

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Solution

Here, x is in quadrant III.

Therefore, and are negative, whereasis positive.

Now,

Thus, the respective values of are.

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Q. If x < 0 and y > 0, then the point (x, y) lies in
(a) quadrant I
(b) quadrant II
(c) quadrant III
(d) quadrant IV

Q. Find the values of the other five trigonometric functions in each of the following:

(i)

\cot x = \frac{12}{5},

x in quadrant III

(ii)

\cos x = - \frac{1}{2},

x in quadrant II

(iii)

\tan x = \frac{3}{4},

x in quadrant III

(iv)

\sin x = \frac{3}{5},

x in quadrant I

Find for , x in quadrant III

c o s x = \frac{- 1}{2}; x \in I I I^{r d}

sin \frac{x}{2}, cos \frac{x}{2} a n d tan \frac{x}{2}

in each of the following:
1:-

tan x = - \frac{4}{3},

I I

cos x = - \frac{1}{3}

, x in quadrant

I I I

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Geometrical Representation of Conjugate of a Complex Number

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