Math

QuestionCalculate the exact value of sin46cos44\sin 46^{\circ} - \cos 44^{\circ} without a calculator.

Studdy Solution

STEP 1

Assumptions1. We are working in degrees, not radians. . We know the trigonometric identities.
3. We know the co-function identity, which states that sin(90x)=cos(x)\sin(90^{\circ}-x) = \cos(x) and cos(90x)=sin(x)\cos(90^{\circ}-x) = \sin(x).

STEP 2

We can use the co-function identity to rewrite the expression.sin46cos44=sin46sin(9044)\sin46^{\circ}-\cos44^{\circ} = \sin46^{\circ}-\sin(90^{\circ}-44^{\circ})

STEP 3

implify the expression in the parenthesis.
sin46sin(9044)=sin46sin46\sin46^{\circ}-\sin(90^{\circ}-44^{\circ}) = \sin46^{\circ}-\sin46^{\circ}

STEP 4

Subtract the two terms.
sin46sin46=0\sin46^{\circ}-\sin46^{\circ} =0So, the exact value of the expression sin46cos44\sin46^{\circ}-\cos44^{\circ} is0.

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