Write each function as an expression involving functions of θ or x alone. See Example 2.
sin(45° + θ)

검증된 단계별 안내

Recall the sine addition formula: \(\sin(A + B) = \sin A \cos B + \cos A \sin B\).

Identify the angles in the expression: here, \(A = 45^\circ\) and \(B = \theta\).

Apply the formula to rewrite \(\sin(45^\circ + \theta)\) as \(\sin 45^\circ \cos \theta + \cos 45^\circ \sin \theta\).

Use known exact values for \(\sin 45^\circ\) and \(\cos 45^\circ\), which are both \(\frac{\sqrt{2}}{2}\).

Substitute these values back into the expression to get \(\frac{\sqrt{2}}{2} \cos \theta + \frac{\sqrt{2}}{2} \sin \theta\).

비슷한 문제에 대한 검증된 영상 답변:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Angle Addition Formula for Sine

The angle addition formula for sine states that sin(a + b) = sin(a)cos(b) + cos(a)sin(b). This allows the expression of the sine of a sum of two angles as a combination of sines and cosines of the individual angles, facilitating simplification or evaluation.

Trigonometric Values of Special Angles

Certain angles like 45° have known exact sine and cosine values, such as sin(45°) = cos(45°) = √2/2. Using these values helps to rewrite expressions involving these angles into simpler numeric forms or functions of the variable angle.

Function Notation and Variable Separation

Expressing a trigonometric function as involving only θ or x means rewriting the expression so that constants and variables are clearly separated, often by substituting known values for constants and leaving the variable angle in function form, aiding clarity and further manipulation.

Write each function as an expression involving functions of θ or x alone. See Example 2.sin(45° + θ)