Question

If cos X=a/b, then sin X is equal to
A. b2-a2/b
B. b-a/b C. √(b2-a2)/b
D. √(b-a)/b

Answer 1

C.

Step-by-step explanation:

$sinx = \sqrt{1 - {cos}^{2}x } \\ = \sqrt{1 - {( \frac{a}{b} })^{2} } \\ = \sqrt{ \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {b}^{2} - {a}^{2} } }{b}$

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ \cos X = \frac{a}{b} }$

TO DETERMINE

The value of sin X

EVALUATION

$\displaystyle \sf{ \cos X = \frac{a}{b} }$

Squaring both sides we get

$\displaystyle \sf{ {\cos}^{2} X = \frac{ {a}^{2} }{ {b}^{2} } }$

$\displaystyle \sf{ \implies \: - {\cos}^{2} X = - \frac{ {a}^{2} }{ {b}^{2} } }$

$\displaystyle \sf{ \implies \: 1- {\cos}^{2} X =1 - \frac{ {a}^{2} }{ {b}^{2} } }$

$\displaystyle \sf{ \implies \: {\sin}^{2} X = \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} } }$

$\displaystyle \sf{ \implies \: {\sin}^{} X = \sqrt{ \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} } }}$

$\displaystyle \sf{ \implies \: {\sin}^{} X = \frac{ \sqrt{{b}^{2} - {a}^{2} }}{ {b}^{} } }$

FINAL ANSWER

$\displaystyle \sf{ {\sin}^{} X = \frac{ \sqrt{{b}^{2} - {a}^{2} }}{ {b}^{} } }$

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