Question

Trig identities?

Answer 1

Find cot θ if \[\csc \theta=\frac{ \sqrt{17} }{ 4 }\] and tan θ > 0.

Answer 2

\[1+\cot ^{2}\theta=\csc^{2}\theta\]

Answer 3

so from the information provided

Answer 4

so cot^2=sqrt(17)/4-1

Answer 5

\[\csc \theta=\frac{ \sqrt{17} }{ 4 }\Rightarrow \csc^2 \theta = \frac{ 17 }{ 16 }\]by squaring both sides

Answer 6

Okay so that would then be 1/16 if you subtract the 1?

Answer 7

\[\cot ^{2}\theta= \frac{ 17 }{ 16 }-1\]

Answer 8

\[\cot ^{2}\theta= \frac{ 1 }{ 16 }\]

Answer 9

take the sqrt of both sides

Answer 10

okay so I was right. so next you sqrt and get cot=sqrt(1)/4

Answer 11

\[\cot=\frac{ \sqrt{1} }{ 4 }\]

Answer 12

take the inverse of the function now and sqrt of 1 is 1

Answer 13

thata = arctan(1/4), now i don't know at your level do you use +-sign or not

Answer 14

yes I do

Answer 15

and do you have to find all solutions, or is the question just on how to use the identity

Answer 16

just that 1/4 was the correct answer

Answer 17

ok good all the best

Answer 18

thank you for you help

Answer 19

but know that later at advanced levels there will be more than one solution for this equation

Answer 20

anytime if you have any question let me know

Answer 21

Just to know, what equation would I use to for Find tan θ if sec θ = sqrt(37)/6 and sin θ < 0.

Answer 22

1+tan^2=sec^2?

Answer 23

the same equation you just used but instead of cot you use tan and instead of csc you use sec

Answer 24

i wrote it this way so you will never forget the identity

Answer 25

okay thanks

Answer 26

you are clever girl you learn quick

Answer 27

i will put the identity for you

Answer 28

\[1+\tan ^{2}\theta=\sec^{2}\theta\]

Answer 29

thanks for all your help!

Answer 30

recall the last identity\[1+\cot ^{2}\theta=\csc^{2}\theta\]

Answer 31

all the best good luck