Question

Find value of Sin 65 cos 38

Answer 1

SOLUTION

TO DETERMINE

The value of

$\sf{ \sin {65}^{ \circ} . \cos {38}^{ \circ} }$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

$\sf{2 \sin \alpha . \cos \beta = \sin ( \alpha + \beta ) + \sin ( \alpha - \beta )}$

EVALUATION

$\sf{ \sin {65}^{ \circ} . \cos {38}^{ \circ} }$

$\displaystyle \: = \sf{ \frac{1}{2} \times 2 \sin {65}^{ \circ} . \cos {38}^{ \circ} }$

$\displaystyle \: \sf{ = \frac{1}{2} \times \bigg[\sin( {65}^{ \circ} + {38}^{ \circ}) +\sin( {65}^{ \circ} - {38}^{ \circ}) \bigg] }$

$\displaystyle \: \sf{ = \frac{1}{2} \times \bigg[\sin {103}^{ \circ} +\sin {27}^{ \circ} \bigg] }$

$\displaystyle \: \sf{ = \frac{1}{2} \times \bigg[0.9743 +0.454 \bigg] }$

$= 0.71415$

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