Trigonomic functions question?

Question

Find the exact value of the remaining trigonomic functions if cos A= -3/5 and sin A < 0.

Answer 1

u know there are some special triangles for trigonometric ratio.

for examples , 1-1-sqrt2 triangle,
1-sqrt3-2 triangle,
3-4-5 triangle.

for ur problem, it is under the category of third triangle.

since cos A is negative, it might be in second or third quadrant.

again, sin A< 0, so, now u can conclude that angle A is in third quadrant.

by considering 3-4-5 triangle, now u can calculate the value of sin A. sin A is -4/5.

so, tan A = (-4/5) * ( -3/5)
=4/3

so cot A = 3/4

sec A = 1/ cos A
= 1/ (-3/5)
= -5/3

cosec A = 1/ sin A
= 1/ ( -4/5)
= -5/4.

Answer 2

The only quadrant where both sin and cos are negative is pi to 3pi/2 (or 180 to 270 degrees).

Get value of other functions from:

Sin A = (-) sqrt (1 - Cos^2 A)
Tan A = Sin A/Cos A
Cosec A = 1/Sin A
Sec A = 1/Cos A
Cot A = 1/Tan A

Answer 3

This describes a 3-4-5 right triangle, so the magnitude of the sine will be 4/5 and the magnitude of the tangent will be 4/3. A sketch will aid in determining the appropriate signs.

Answer 4

you may desire to employ what are called trigonomeric identities. an entire record of those could desire to be on your text cloth e book....i do no longer bear in innovations all of them and this is been years on account that I had a trig e book, yet there are somethings I bear in innovations. Like sin^2x + cos^2x = a million. so sin^2x = a million-cos^2x. And substituting this back into concern a million provides us: cosx -2(a million-cos^2x) +a million = cosx-2 +2cos^x + a million= cosx -a million + 2cos^2x and rearranging phrases: 2cos^2x +cosx-a million.....this is factored as follows: (2cosx-a million)(cosx+a million)....of what value this is, i don't recognize. for concern 2, use identities cot x = a million/tan x and csc x = a million/cos x and perform a little substitution to get: 4tan^2x-4 tanx +sin x/cos x yet sin x/cos x is tan x so which you have: 4 tan^2x - 4 tan x + tan x = 4 tan^2 x -3tan x or tan x(4 tan x -3) so as that's a thank you to proceed. locate the main appropriate identity, do the substitution, and then deliver jointly like phrases, simplify, and ingredient.

Answer 5

cos A=-3/5
cos A= ad/hypo

5 /|
-- -3

5*5-3*3=16 = 4*4

5 / |4
-- -3

sin=opposi/hypo
oppo=4...hypo=5
so
Sin A= 4/5

ha!

Answer 6

From given info. angle is in 3rd quadrant>
sin A = - 4/5
tan A = (- 4) / (- 3) = 4 / 3

Answer 7

1-cos²A = sin²A so
1-9/25 = 16/25 and
sin²A = 16/25 so that (taking the negative root)
sinA = -4/5
Since tanA = sinA/cosA then
tanA = (-4/5)/(-3/5) = 4/3

HTH

Doug

Answer 8

cos A= -3/5
A = 128.9, 360-128.9
A = 128.9, 231.1