Question

what does this mean?

Answer 1

The cosine value of some angle theta =0.7673

Answer 2

yeah

Answer 3

what do I do with the interval given?..

Answer 4

hmm what's the \(cos(180^o)\quad ?\)

Answer 5

the interval given is just a range within which the angle must lie

Answer 6

so say for example... what would be the \(cos(180^o)\quad ?\)

Answer 7

Is there more than 1 angle in this interval?

Answer 8

oh -1 ?

Answer 9

right....
so now, what's the \(cos^{-1}(-1)\quad ?\)

Answer 10

isn't it just pi?

Answer 11

yes, pi or \(180^o\) so.. what does that mean? well
it means that \(\bf cos(\pi)=-1\qquad cos^{-1}(-1)=\pi\qquad \qquad cos^{-1}[cos(\pi)]=\pi\)

Answer 12

k go it

Answer 13

\(\bf cos(\theta)=x\qquad cos^{-1}(x)=\theta\qquad \qquad cos^{-1}[cos(\theta)]=\theta\)

Answer 14

so... \(\bf cos(\theta)=0.7673\qquad \textit{take }cos^{-1}\textit{ to both sides}\\ \quad \\
cos^{-1}[cos(\theta)]=cos^{-1}(0.7673)\implies \theta=cos^{-1}(0.7673)\)

Answer 15

oh!

Answer 16

so i solve for cos^-1(0.7673)?

Answer 17

yeap, and that'd give you an angle whose cosine is 0.7673

Answer 18

i got 0.6961... = 0.7 = 40° ? or .. 39.89°

Answer 19

it sayto round to the nearest hundreths so .69617.. = .70

Answer 20

yeap, I got the same..... so that'd be a value where the cosine is positive, which is in the 1st Quadrant
now keep in mind the cosine is also positive in the 4th Quadrant, so the reference angle at the 4th Quadrant is another angle whose cosine function is also 0.7673

Answer 21

... to the nearest hundredth then it'll be 39.89 and 360-39.89 = 320.11

Answer 22

wait so the answer that my question wanted wasn't in degrees or is it since thetha?

Answer 23

ok yeah i see :)

Answer 24

well... it doesn't specify, but you can always convert to radians if you wish, by \(\bf radians=\cfrac{degrees\cdot \pi}{180}\)

Answer 25

k ty

Answer 26

yw