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What is the value of sin(30°) * cos(60°) + cos(30°) * sin(60°)?
0
0.5
1
0.866
1
Recognize the identity for the sine sum formula, sin(A+B). Here A=30° and B=60°, so the expression is simply sin(30°+60°)=sin(90°)=1.
Expression to evaluate: sin(30°) * cos(60°) + cos(30°) * sin(60°)
sin(A+B)=sin(A)cos(B)+cos(A)sin(B)
Recognize the identity for the sine sum formula, sin(A+B). Here A=30° and B=60°, so the expression is simply sin(30°+60°)=sin(90°)=1.
Many students waste time calculating individual trigonometric values (e.g., 1/2∗1/2+3/2∗3/2) instead of recognizing the standard sine addition identity, which leads to arithmetic errors.
Identify the pattern
The given expression fits the standard trigonometric addition formula for sine: sin(A)cos(B)+cos(A)sin(B)=sin(A+B).
sin(A)cos(B)+cos(A)sin(B)=sin(A+B)
Substitute values
Substitute A=30° and B=60° into the identity formula.
sin(30°+60°)=sin(90°)
Calculate final result
Since the value of sin(90°) is 1, the result of the entire expression is 1.
sin(90°)=1
C is correct because the expression simplifies to the identity sin(90°), which equals 1.
This identity is a fundamental building block for solving problems in Wave Optics and Phase Difference calculations in Physics, where superposition of waves occurs.
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