Question

NEED HELP WITH PRE-CAL/TRIG PROBLEM (PIC INSERTED)

Answer 1

does it help to know that
\[\sin(\frac{3\pi}{2})=-1\] ?

Answer 2

yea but what do i do with the tangent part

Answer 3

find an angle (number) \(x\) between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) with \(\tan(x)=-1\)

Answer 4

that is what
\[\tan^{-1}(-1)\] means

Answer 5

okay but im still not seeing the whole picture ..

Answer 6

should i just plug that in the calculator?

Answer 7

no

Answer 8

think of a place on the unit circle where sine and cosine have the same value except they are of opposite sign

Answer 9

7pi/4

Answer 10

hint, one is \(\frac{\sqrt{2}}{2}\) and the other is \(-\frac{\sqrt{2}}{2}\)

Answer 11

and pi/4

Answer 12

no not pi/4
there they are both positive

Answer 13

okay

Answer 14

and while \(\frac{7\pi}{4}\) would work, that is not the answer because that is not in the interval \([-\frac{\pi}{2},\frac{\pi}{2}]\)

Answer 15

\[\sin \frac{ 3\pi }{2}=\sin \left( \pi+\frac{ \pi }{2} \right)=-\sin \frac{ \pi }{ 2 }=-1\]
\[\tan^{-1} \left( -1 \right) =\pi-\frac{ \pi }{ 4 },\left( 2\pi-\frac{ \pi }{ 4 } \right)=\frac{ 3\pi }{ 4 },\frac{ 7\pi }{4 }\]

Answer 16

those are not the answers either, unfortunately

Answer 17

im confused now

Answer 18

you have to pick a number in the right interval
the range of arctangent is \([-\frac{\pi}{2},\frac{\pi}{2}]\)

Answer 19

ok 3pi/4

Answer 20

name that angle

Answer 21

315 degrees

Answer 22

no \(\frac{3\pi}{4}\) it too big

Answer 23

hint: it is NEGATIVE

Answer 24

-45 degrees

Answer 25

yes!

Answer 26

except you should answer in radians

Answer 27

\(-\frac{\pi}{4}\) is the correct answer

Answer 28

ohh okay

Answer 29

\[if you want the answer \in [\frac{ -\pi }{ 2 },\frac{ \pi }{ 2 }],then \it is \frac{ -\pi }{ 4 }\]

Answer 30

thank you both ...

Answer 31

i used to be a wiz at this pellet ... now i forgot how to do everything with pre cal

Answer 32

it is not really a matter of "what you want' the range of arctangent is in that interval, no other answer will do

Answer 33

been focusing too much on stats