Find the values of the trigonometric function cot -8/17

sin:
sec:
tan:
cot:

I know you use a Pythagorean Identity, sin^2t + cos^2t=1

I got 64/289 for the first one for example and it was wrong.

Your terminology is awful

cot - 8/17 is meaningless

I will assume you were given cot Ø = -8/17 and are asked to find the remaining 5 trig ratios

if cot Ø = -8/17, then tan Ø = -17/8

you should also have memorized the 3 main trig functions in terms of x, y, and r
e.g. tan Ø = y/x = -17/8 ---> terminal point (8, -17)
or
tan Ø = y/x = 17/-8 ----> terminal point (-8,17)


From the CAST rule we know that Ø must be either in quadrants II or IV , as seen from the position of the terminal arm points.
so make appropriate sketches showing right-angled triangles .

x^2 + y^2 = r^2 , taking one of the points
r^2 = 8^2 + (-17)^2
r^2 = 353
r = √353 , (r is always positive)

sinØ = y/r = 17/√353 or sinØ = 17/√353
cosØ = ±8/√353 so
secØ = ± √353/8
etc using the basic definitions.

Let me know if my assumption was not correct

To find the values of trigonometric functions, such as cot, we need to use the definitions and relationships between the trigonometric functions.

To start, let's recall the definitions of some trigonometric functions:

- Sine (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.
- Cosine (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle.
- Tangent (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.
- Cotangent (cot) is defined as the reciprocal of the tangent function, so cot x = 1/tan x.

Now, let's focus on the specific problem. We need to find the value of cot(-8/17).

1. First, let's find the value of tan(-8/17):

Given that tan x = sin x / cos x, we can find the values of sin(-8/17) and cos(-8/17). The Pythagorean Identity sin^2x + cos^2x = 1 will not directly help here.

2. To find sin(-8/17), we notice that sin x = -sin(-x) for any angle x. So, sin(-8/17) = -sin(8/17).

3. Similarly, to find cos(-8/17), we notice that cos x = cos(-x) for any angle x. So, cos(-8/17) = cos(8/17).

4. We can calculate sin(8/17) and cos(8/17) by using a calculator or trigonometric tables.

5. Once we have sin(8/17) and cos(8/17), we can find tan(-8/17) by the formula mentioned earlier: tan(-8/17) = sin(-8/17) / cos(-8/17).

6. Now, we can find cot(-8/17) by taking the reciprocal of tan(-8/17). So, cot(-8/17) = 1 / tan(-8/17).

To summarize, to find the values of trigonometric functions, we need to use the definitions and relationships between the functions. In the provided example, you can find cot(-8/17) by following the steps above.