Question

Can i get some help with this, Please?

Given cos theta=24/25 and is located in Q3, Evaluate the rest of the trigonometric functions:
1. sin theta=
2. tan theta=
3. cot theta=
4. sec theta=
5. csc theta=

Answer 1

sin^2 + cos^2 = 1

sin^2 + (24/25)^2 = 1

sin^2 + 576/625 = 1

sin^2 = 1 - 576/625

sin^2 = 49/625

sin = sqrt(49/625)

sin = 7/25


Since we're in Q3, sine theta is negative, so sin theta = -7/25


So when cos theta=24/25, sin theta = -7/25

Answer 2

eh, that looks confusing. So for tan theta, would i start off as tan^2+cos^2

Answer 3

tan = sin/cos

Answer 4

that's one of the definitions of tangent

Answer 5

oh yeah, i remember that. So what do i do next?

Answer 6

tan = sin/cos

tan = (-7/25)/(-24/25)

tan = (-7/25)*(-25/24)

tan = 7/24


Note: cosine should be negative as well in Q3...not sure why they made it positive

Answer 7

So is there a reason why you swapped (-24/25) to (-25/24) or does it matter?

Answer 8

(a/b) divided by (c/d)

is the same as

(a/b) times (d/c)

Answer 9

when you divide fractions, flip the second fraction and multiply

Answer 10

Oh ok. So im a little familiar with tan, cos, and sin. But not with cot,csc, and sec.

Answer 11

cot = 1/tan

csc = 1/sin

sec = 1/cos

all by definition

Answer 12

so if tan = a/b, then cot = b/a (you flip the fraction...ie find the reciprocal)


In this case,

tan = 7/24

so

cot = 24/7

Answer 13

so times cot by cos?

Answer 14

no, you take whatever tan is and you flip it to get cot

Answer 15

oh, pretty easy.

Answer 16

yeah it's not too bad once you get the hang of it

Answer 17

the trick is remembering what cot, csc and sec stand for (and what they equal)

Answer 18

so sec=1/cos so sec=1/(24/25)?

Answer 19

yes, but cosine should be negative

Answer 20

so sec = 1/(-24/25) ----> sec = -25/24

Answer 21

and the last one is csc theta= what does csc even mean? Like tan=tangent.

Answer 22

cot = cotangent

csc = cosecant

sec = secant

Answer 23

So for csc...

1/(-7/25) ?

Answer 24

yes, which becomes

csc = -25/7

Answer 25

Your so much help. Thank you so so much.

Answer 26

you're very welcome