MathUp Evaluating Expressions
1 answer:
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Answer with explanation:
It is given that for three integers , a, b and c, if
Since , a b is divisible by c , following are the possibilities
1.→ a and b are prime integers .Then , c will be prime number either equal to a or b.
2.→a and b are not prime integers ,then any of the factors of a or b will be equal to c.For example:
⇒a=m × n
b=p × q× c
or,
⇒a=u×v×c
b=s×t
So, whatever the integral values taken by a, and b, if then either of
is true.
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Answer:
- sin(Ф) = (4/41)√41; csc(Ф) = (√41)/4
- cos(Ф) = (5/41)√41; sec(Ф) = (√41)/5
- tan(Ф) = 4/5; cot(Ф) = 5/4
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you with three of the functions. Then you need to remember the relations between those and the other three.
Tan = Opposite/Adjacent
tan(Ф) = 4/5
This suggests you can draw a triangle like the one attached that has adjacent side 5 and opposite side 4. Then hypotenuse can be found from the Pythagorean theorem:
AC² = AB² +BC² = 5² +4² = 41
AC = √41 . . . . . hypotenuse
Then the other trig functions are ...
Sin = Opposite/Hypotenuse
sin(Ф) = 4/√41 = (4/41)√41
Cos = Adjacent/Hypotenuse
cos(Ф) = 5/√41 = (5/41)√41
And the reciprocal functions are ...
csc(Ф) = 1/sin(Ф) = (√41)/4
sec(Ф) = 1/cos(Ф) = (√41)/5
cot(Ф) = 1/tan(Ф) = 5/4
