Question

Approximate, to the nearest 0.01 radian, all angles θ in the interval [0, 2π) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a)
sin θ = −0.0134

θ =

(b)
cos θ = 0.9238

θ =

(c)
tan θ = 0.46

θ =

(d)
cot θ = −2.771

θ =

(e)
sec θ = −3.5

θ =

(f)
csc θ = 1.22

θ =

Answer 1

Assuming we are in radians right

Answer 2

Yes

Answer 3

well first thing to do is graph and set window from what i think is 0 to 2pi

and the Y axis of the window from -1 to 1

You can typically do this to graph

trigfunction(x)=a

trigfunction(x)-a

for example one you can do this

sin θ = −0.0134
sin(x)- −0.0134

answer will be where the curve touches zero on the interval
[0, 2π)
include zero not including 2pi

https://www.google.com/?gws_rd=ssl#q=sin(x)+%E2%88%92+0.0134

Answer 4

okay, how would i do that for the ones that arnt sin cos tan though?

Answer 5

it works for all of them including
Sec csc cotan

Answer 6

Okay can you give me an example of one?

Answer 7

there is a better way i think without relying on graph. Graph is just a visual way. Hold on its been a while

Answer 8

Okay, yeah because when i put in my graphing calculator it didn't make much sense to me

Answer 9

it does it just that you probably have your window too big or small or just not the right scale.

Answer 10

wait what would i be putting for y=

Answer 11

Here is an example for the first one

MAKE SURE YOU IN RADIANS BTW

sin θ = −0.0134

all your qs are in an an easy way where you just take the arctrigfunction

here it is sin theta for simplicity purposes i will replace your θ with an x. Know it is the same thing i just using a different variable.


so you got sin so apply arcsin to both sides like this. OR sin^-1 same thing just that different calculators use different key labels.


arcsin( sin x) = arcsin(-0.0134)
x= arcsin(-0.0134) notice that arcsin made sin dissapear and you left with just x

x=-0.1340040105e-1 now you just evaluate the right hand side.



we not done yet but you with me so far?

Answer 12

since you want only the interval from [0, 2π) Read as include zer0 but not 2 pi

One of your answers was -0.1340040105 But it is below zero. However If i remember right trig functions repeat every 2pi intervals so

2pi+(-0.1340040105) Is in that interval

2pi+(-0.1340040105)+2pi is not i think