# Find the remaining trigonometric ratios of θ if csc(θ) = -6 and cos(θ) is positive

Answer: Now, the cosecant of θ is -6, or namely -6/1.

however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.

we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

recall that

therefore, let's just plug that on the remaining ones,

now, let's rationalize the denominator on tangent and secant,

## Related Questions

rectangle with a perimeter of 60 feet has a length and width in a ratio of 3:2. What are the length and width?

Total parts:
3+2= 5

Half of perimeter (or the sum of the length and the width) is:
60 ft/2= 30 ft

Each part is:
30 ft/ 5 parts= 6 ft/part

The length costs 3 parts, and the length is:
6 ft/ 1 part* 3 parts= 18 ft.

The width costs 2 parts, and the width is:
6 ft/ 1 part* 2 parts= 12 ft.

The length and the width of the rectangle are 18 ft and 12 ft respectively~

Can 29/48 be simplified

29/48 Can not be simplefied... Nothing will go into 48 that can also go into 29.
Well actually we can't simplified or reduce more the final answer is 29/48 :)

Please help! Determine if the function shows a linear relationship or an absolute value relationship. Then evaluate the function for the indicated value of x.
a. f(x) = |x – 3| – 2; x = –5
b. g(x) = 1.5x; x = 0.2
c. p(x) = |7 – 2x|; x = –3

(a) Absolute value relationship, f(-5)=6

(b) Linear relationship, g(0.2)=0.3

(c) Absolute value relationship, p(-3)=13

Step-by-step explanation:

A modulas function always represents an absolute value relationship.

A polynomial function with degree 1 is always represents a linear function.

(a)

The given function is

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-5 in the given function.

Therefore the value of function at x=-5 is 6.

(b)

The given function is

It is a linear function, so it represents a linear relationship.

Substitute x=0.2 in the given function.

Therefore the value of function at x=0.2 is 0.3.

(c)

The given function is

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-3 in the given function.

Therefore the value of function at x=-3 is 13.

I think it’s b:g(x)=1.5x; x=0.2

Jim borrows \$14,000 for a period of 4 years at 6 % simple interest. Determine the interest due on the loan. [4 marks