Question

Find the exact value of the remaining trig functions:
sec theta=-5/4, tan theta<0

Answer 1

\[\cos(\theta) = -4/5\]

Answer 2

using that, we can get all the other ratio values

Answer 3

\[\sin(\theta)=3/5\]\[\cos(\theta)=-4/5\]\[\tan(\theta)=-3/4\]\[\csc(\theta)=5/3\]\[\sec(\theta)=-5/4\]\[\cot(\theta) = -4/3\]

Answer 4

How do I find all of them?

Answer 5

Use the trig identity: sec^2 x = 1 + tan ^2 x . Find the arc x knowing sec x = -5/4.
25/16 = 1 + tan^2x --> tan^2 x = 25/16 - 16/16 = 9/16
tan x = -3/4 and tan x = 3/4.
Calculators will give 2 values of x. The answer that gives sec = -5/4 will be selected.

Answer 6

o = opposite
a = adjacent
h = hypotenuse

sin(θ) = o/h
cos(θ) = a/h
tan(θ) = o/a
csc(θ) = h/o
sec(θ) = h/a
cot(θ) = a/o

Answer 7

do you know SOHCAHTOA?

Answer 8

That's basically all I know.

Answer 9

take a look at this then: http://www.math.uci.edu/sites/math.uci.edu/files/trig.pdf

Answer 10

Just the left portion of the first page

Answer 11

nvm, just look at this instead

Answer 12

going back to your original question, sec(θ) = 1/cos(θ)
so, cos(θ) = -4/5

Answer 13

cos theta=1/sec theta=-1/5/4=-4/5
For sin theta use:
sin^2 theta+cos^2 theta=1
Put the value for cos theta and get sin theta. After you get sin theta use 1/sin theta to get cosec theta.
After you get the values of sin theta and cos theta, you can get the value of tan theta by using:
tan theta= sin theta/cos theta.

Good luck