Answer:
sinФ = 8/17
cosФ = 15/17
tan Ф = 8/15
csc Ф = 17/8
sec Ф = 17/15
cot Ф = 15/8
Step-by-step explanation:
Let us revise the trigonometry functions
- Sin(x) = opposite/hypotenuse
- Cos(x) = adjacent/hypoteouse
- Tan(x) = opposite/adjacent
- Csc(x) = hypotenuse/opposit
- Sec(x) = hypotenues/adjacent
- Cot(x) = adjacent/opposite
In the given figure
The opposite side to angle Ф = 8
The adjacent side to angle Ф = 15
Find the hypotenuse using Pythagoras' theorem




Let us use the rules above to find the trigonometry functions
sinФ = 8/17
cosФ = 15/17
tan Ф = 8/15
csc Ф = 17/8
sec Ф = 17/15
cot Ф = 15/8
Answer:
k = 2
Step-by-step explanation:
Use a graphing calculator
Each curve completes one loop over the interval

. Find the intersections of the curves within this interval.

The region of interest has an area given by the double integral

equivalent to the single integral

which evaluates to

.
A conservative vector field

has curl

. In this case,

so the vector field is not conservative.
16/3 is rational simply because it is a fraction made up of whole numbers.
Irrational numbers cannot be expressed as fractions made up of whole numbers.