i-express-the-function-f-sin-cos-in-the-form-rsin-r-gt-0-and-0-pi-2-ii-hence-find-the-maximum-value-of-f-and-the-smallest-non-negative-value-of-at-which-it-occurs-

Question Number 10746 by okhema last updated on 24/Feb/17

i) e x p r e s s t h e f u n c t i o n f (θ) = s i n θ + c o s θ i n t h e f o r m r s i n (θ + α), r > 0 a n d 0 ⩽ θ ⩽⩽ \frac{π}{2}

i i) h e n c e f i n d t h e m a x i m u m v a l u e o f f a n d

t h e s m a l l e s t n o n - n e g a t i v e v a l u e o f θ a t w h i c h i t o c c u r s .

Answered by mrW1 last updated on 24/Feb/17

i)

f (θ) = s i n θ + c o s θ = \sqrt{2} (s i n θ \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} c o s θ) = \sqrt{2 (} s i n θ \cos \frac{π}{4} + c o s θ \sin \frac{π}{4})

= \sqrt{2} \sin (θ + \frac{π}{4})

i i)

m a x . f (θ) = \sqrt{2} w i t h θ = \frac{π}{4}

m i n . f (θ) = 1 w i t h θ = 0 o r \frac{π}{2}

Facebook Tweet Pin