expressf-8cos-15sin-in-the-form-rcos-where-r-gt-0-and-is-a-positive-acute-angle-hence-find-the-general-solution-of-the-equation-80cos-150sin-13-the-maximum-and-minimum-value-

Question Number 73544 by Rio Michael last updated on 13/Nov/19

e x p r e s s f (θ) = 8 c o s θ - 15 s i n θ i n t h e f o r m

r c o s (θ + α), w h e r e r > 0 a n d α i s a p o s i t i v e a c u t e a n g l e

h e n c e

f i n d t h e g e n e r a l s o l u t i o n o f t h e e q u a t i o n

80 c o s θ - 150 s i n θ = 13

t h e m a x i m u m a n d m i n i m u m v a l u e o f \frac{5}{f (θ) + 3}

Answered by mind is power last updated on 13/Nov/19

8 c o s (θ) - 15 s i n (θ) = 17 {\frac{8}{17} c o s (θ) - \frac{15}{17} s i n (θ)}

= 17 c o s (θ + a r c o s (\frac{8}{17}))

α = a r c o s (\frac{8}{17})

80 c o s (θ) - 150 s i n (θ) = 170 c o s (θ + α) = 13

c o s (θ + α) = \frac{13}{170}

θ + α = \underline{+} a r c o s (\frac{13}{170}) + 2 k π

m i n a n d m a x d i d n t e x i s t

s i n c e f (θ) = - 3 h a s e s o l u t i o n

Commented by Rio Michael last updated on 13/Nov/19

w o n d e r f u l s i r