Question

if cosec A = √10 , find other five trigonometric ratios

Answer 1

coseca =✓10
coseca=1/sina
sina =1/✓10
sina =opp side/hyp=1/✓10
so hyp is ✓10 and one side is 1
according to pythogoras theorem,
side^2 +side^2=hyp^2 so
1^2+side^2=✓10^2
1+side^2=10
side^2=10-1=9
side equals 3 which is adj side
Cosa=adj side/hyp =3/✓10
tana equals sina/Cosa
tana=1/3
cota =1/tana=3
seca=1/Cosa=✓10/3

Answer 2

If cosec A = √10.

construct a triangle that has that cosec A as that value.

cosec = 1/sin = 1/(opp/hypo) = hypo/opp.

Hence the triangle would have side 1 and hypotenuse √10. Plugging into the Pythagorean theorem, one can see that the other side is 3. With that out of the way, we can start constructing the other 5 trig ratios. We should also state that we are assuming all angles to be within quadrant 1, otherwise we might be dealing with negatives.

Opposite = 1

Adjacent = 3

Hypotenuse = √10

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$sin = opp./hyp. = 1/(root10) = (root10) /10$

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$cos = a/h = 3/(root10) = 3*(root10) /10$

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$tan = opp./adj. = 1/3$

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$sec = (root10) /3$

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$cot = 3/1 = 3$

MAY THIS HELP U MY FRND!!!