if cos theta =4/5, what is sin and tan theta? if tan theta=c, express sin and cos theta in terms of c?

Answer 1

Well...you have to use pythagorean theorem for this. the 5 (r) is the C, and the 4 (y) is one of the sides. Now use A^2 + B^2 = C^2 to find the other side. Whatever the number is, put it over 5 and that will be your sin. Then Tangent is simply y/x.

Answer 2

I will refer to theta as x for simplicity

cos x = 4/5
sin x = sqrt(1-(4/5)^2)
= ±3/5

tan x = sin x / cos x
=±3/4


tan x = c
Draw a right angled triangle.
Perpendicular = c
Base = 1
Hypotenuse = sqrt(1+c^2) ----- Pythagoras' Theorem
We are not sure of the sign so allow both positive values and negative values.

sin x = ±c/(1+c^2)
cos x = ±1/(1+c^2)
tan x = c

Answer 3

When you see 4 and 5 you should immediately think 3-4-5 right angle

cos theta = 4/5
sin theta = 3/5
tan theta = 3/4

if tan theta = c then sin theta = 4/5c and cos theta = 16/15c

Answer 4

You are going to see LOTS of examples of triangles that have sides in multiples of 3,4 and 5. This is a right triangle
One side is 3, one is 4 and the hypotenuse is 5

So, if the cosθ=4/5, then sinθ=3/5, and tanθ=3/4
If the cosθ=3/5, the sinθ=4/5, and tanθ=4/3
It doesn't make any difference if one or more of the functions is negative, you're still working with a "3-4-5" triangle. They'll try to confuse you by trying to hide the fact. They'll say tanθ=.75, or that secθ=1.25. They'll say one side is 15 and the other 20 trying to get you to think, "ah-ha... 15 divisible by 5... short side... not hypotenuse... not "3-4-5" triangle. It'll be on exams. It'll be on entrance tests.

Not exactly certain what you're looking for in the second part of the question.
sinθ/cosθ=tanθ
If tanθ=c, then
sinθ/cosθ=c
sinθ= (c)cosθ . . . . . . . . . . 3/5=3/4x4/5 works for example
cosθ = (sinθ)/c . . . . . . . . . .4/5=3/5x4/3 works for example

Or you might mean,
tanθ=c = c/1
Then the hypotenuse would be √(c² + 1)
So sinθ = c/√(c² + 1), or c√(c² + 1)/(c² + 1)
and cosθ = 1/√(c² + 1), or √(c² + 1)/(c² + 1)

Answer 5

You should be able to figure this stuff out for yourself. If cos O = 4/5, you are dealing with a 3/4/5 right triangle. Figure the others out for yourself. Since tan O = opposite/adjacent sides, if you set the adjacent side equal to 1, the opposite side is c and the hypotenuse is
sqrt(1+c^2). Sin is c/sqrt(1+c^2) and cosine is 1/(1+c^2). Now go back and get those definitions down cold.

Answer 6

cos x = side adjacent/hypotenuse = 4/5

Now we now that the triangle is a 3, 4, 5 right triangle

then sin theta = 3/5

and tan theta = 3/4

tan theta = c = sin theta / cos theta

sin theta = c * cos theta
cos theta = (sin theta) / c
.

Answer 7

its a 3,4,5 right triangle sin= 3/5 tan=3/4

i have no idea of the other question

Answer 8

Use x in place of theta 1. sec x = 1/ cos x ...............................Ans 2. tan x = sin x / cos x...................................Ans 3. cot x = cos x/ sin x.....................................An... 4. cosec x = 1/ sin x..........................................