Question

Find all solutions of the equation that lie in the interval [0,pie] state each answer correct to two decimal places
csc=5
If there is more then one solution, separate your answers with commas

Answer 1

not without a calculator
your job is to find
\[\csc(x)=5\]
\[\frac{1}{\sin(x)}=5\]
\[\sin(x)=\frac{1}{5}\] now i doubt you know a number whose sine is 1/5 so you need
\[\sin^{-1}(\frac{1}{5})=x\] and a calculator to sovle it

Answer 2

so .20?

Answer 3

no. what satellite is saying is... what x, between 0 and pi, will give you sin (x) = .2. you'll need your calculator (or a table of trig values) that will give .2 as the sine of that number.

Answer 4

which would be...

Answer 5

x=arcsin(1/5) this is the exact answer... approximately equal to 0.20135. Now to check if this is correct, try taking sin(0.20135). You should get somewhere close to .2. Make sure your calculator is in radian mode.

Answer 6

which the answer would be .20

Answer 7

didn't even notice that. yep.

Answer 8

but remember, you're looking at the range from 0 to pi. so, since .20 radians is in the first quadrant, the sine is equal in the second quadrant also. so to get the other answer, take pi-0.20135. this should also be an answer.

Answer 9

so approx 2.94

Answer 10

yes..

Answer 11

what about cos=-.4

Answer 12

cos(x)=-0.4 this is the same as
x = arccos(-0.4) which is about 1.98. is the requirement for your answer to still be between 0 and pi?

Answer 13

yes