Question

how do you factor a trigonometric function

Answer 1

well it depends what it looks like

if you had

2sin^2(x) + 3sin(x) + 1 = 0

it factors like a quadratic

(2sin(x) + 1)(sin(x) + 1) = 0

etc..

Answer 2

same way you factor a polynomial function, instead of variables you have trig functions

Answer 3

thanks guys, i already figured out how, sorry to waste your time

Answer 4

but i do need help with something else

Answer 5

Find sin θ if cot θ = - 4 and cos θ < 0.
no answer please, i just want to know how to do it, if you do have the answer please show the steps

Answer 6

ok for these type of problems I like to draw a triangle

first determine which quadrant theta is in:
cos < 0 --> Q2,Q3
cot <0 so tan <0 --> Q2,Q4
therefore we are in Q2 so sin is positive

Answer 7

so 1 over sqrt of 17 right?

Answer 8

correct

Answer 9

but thats not an option

Answer 10

well im 100% sure it is correct so either the textbook is in error or its written a different way

Answer 11

do you know how to rationalize the denominator (get rid of the sqrt)

Answer 12

they have sqrt of 17 over 4?

Answer 13

no that is not equal to 1/sqrt17

Answer 14

\[\frac{1}{\sqrt{17}}*\frac{\sqrt{17}}{\sqrt{17}} = \frac{\sqrt{17}}{17}\]

Answer 15

they have that

Answer 16

thanks

Answer 17

yw

Answer 18

do you think you could help me with one more problem

Answer 19

ok but if its similar i will refer you to my answer to this problem

Answer 20

ok

Answer 21

quantity cosecant of x to the power of two times secant of x to the power of two divided by quantity secant of x to the power of two plus cosecant of x to the power of two.

Answer 22

csc^2(x) * sec^2(x) /sec^2 (x) + csc^2(x)

Answer 23

simplify

Answer 24

ok start by substituting
csc = 1/sin
sec = 1/cos

then combine the fractions in the denominator

Answer 25

but isnt that only if they werent squared

Answer 26

doesn't matter

csc^2 = 1/sin^2
sec^2 = 1/cos^2

Answer 27

ok and that equals 1

Answer 28

well sin^2 + cos^2 = 1, is that what you mean?

Answer 29

yes

Answer 30

and 1/1 =1

Answer 31

now its 1/sce^2(x)*csc^2(x) right

Answer 32

no you lost me

csc^2 +sec^2 is not the same as sin^2 +cos^2

Answer 33

just sub everything in and work through it step by step

Answer 34

no im talking about the denominator

Answer 35

ok hld on let me try this

Answer 36

oh i see ....yes you got it however it should be 1/sin^2 cos^2

Answer 37

ok thanks!

Answer 38

you are correct, answer is 1
sorry i hadn't worked it out yet