Question

assignment 9.2: sum and difference identities
score: 7/8 answered: 7/8
question 8
simplify without a calculator:
\\( \sin ( 38 ^ { \circ } ) \cos ( 52 ^ { \circ } ) + \cos ( 38 ^ { \circ } ) \sin ( 52 ^ { \circ } ) \\)
\\( = ? \\) ( )
\\( = \\)
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Explanation:

Step1: Use the sum formula for sine

The sum formula for sine is $\sin(A + B)=\sin A\cos B+\cos A\sin B$.
Here, $A = 38^{\circ}$ and $B = 52^{\circ}$.
So, $\sin(38^{\circ})\cos(52^{\circ})+\cos(38^{\circ})\sin(52^{\circ})=\sin(38^{\circ}+ 52^{\circ})$.

Step2: Calculate the sum of angles

Calculate $38^{\circ}+52^{\circ}=90^{\circ}$.
Then, $\sin(90^{\circ}) = 1$.

Answer:

$\sin(90^{\circ})$; $1$