Question

HELP : Part (ii) (b)

(i) Express (√6) cos θ + (√10) sin θ in the form R cos(θ − α ), where R > 0 and 0◦< α < 90◦. Give
the value of α correct to 2 decimal places.
(ii) Hence, in each of the following cases, find the smallest positive angle θ which satisfies the
equation
(a) (√6) cos θ + (√10) sin θ = −4,
(b) (√6) cos1/2θ + (√10) sin1/2θ = 3

Answer 1

@hartnn @thomaster

Answer 2

do you know the expansion of cos(theta-alpha) ?

Answer 3

i just need help for ( ii) part (b)

Answer 4

is it theta/2 or 1/(2theta)

Answer 5

\[4 \cos \left( \theta/2 - \alpha \right) = 3\]
\[\alpha = 53.238..\]

Answer 6

\[\left( \theta/2 - \alpha \right) = \cos^{-1} \frac{ 3 }{ 4 }\]

Answer 7

yeah you are right.............now substitute the values

Answer 8

theta / 2 = cos inverse 3/4 + alpha...
theta = 2 ( cos inverse 3/4 + alpha)
= 189.2952

Answer 9

but thats not the right answer :S

Answer 10

let me check a moment

Answer 11

@satellite73

Answer 12

k i got it

Answer 13

theta - alpha/2 can be negative also

Answer 14

its just : theta /2
not alpha...

Answer 15

sry.......theta/2 - alpha can be negative also....................you know cos ^-1(3/4) is also -41.4

Answer 16

try this value you will get your answer.........i expect the answer is 23.6

Answer 17

yep but the answer should be : 21.7 ~_~

Answer 18

(Y) ! :D

Answer 19

but one more question : how do we know when to take negative for cos-1 ?

Answer 20

why take negative of cos inverse rather than positive o.o ?

Answer 21

in this case you should check with both to see which one is giving you the smallest angle.........because the question says find smallest positive angle

Answer 22

suppose the question was to find all values of theta then i should take cos both positive and neg ?

Answer 23

yup.......and if the question is to find ALL the values of theta, then there are several answers.....remember trigonometric functions start repeating again and again

Answer 24

:D ty :D !