Question

4. Find the range of the following functions :
(i) f(x) = 2 - 3 cos x
(ii) f(x) = 2 +5 sin 3x
6. In which quadrant does x lies if
(1) cos x is positive and tan x is negative
(ii) both sin x and cos x are negative
(ii) sin x =4/5 and cos x=-3/5

(iv) sin x = 2/3 and cos x= -1/3?
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Answer 1

Answer:

Step-by-step explanation:

we \: know \: that \: \\ - 1 \leqslant \sin(3x) \leqslant 1 \\  

now multiplying by -1 we get,

=> 1 ≥ - sin3x ≥ -1  

adding 2 we get,

=> 2+1 ≥ 2 - sin3x ≥ 2-1  

=> 3 ≥ 2-sin3x ≥ 1  

now taking inverse we get,  

\frac{1}{3} \leqslant \frac{1}{2 - \sin(3x) } \leqslant 1

so Range € [ ⅓ , 1 ]