To find the value of sin(37°) * sin(53°) * tan(37°) * tan(53°), we can make use of some trigonometric identities and properties.
First, let’s recall that:
- sin(53°) can be expressed as sin(90° – 37°) = cos(37°)
- tan(53°) can be expressed as tan(90° – 37°) = cot(37°)
Now, substituting these into our expression:
sin(37°) * sin(53°) * tan(37°) * tan(53° becomes:
sin(37°) * cos(37°) * tan(37°) * cot(37°)
Since tan(37°) = sin(37°)/cos(37°) and cot(37°) = cos(37°)/sin(37°), we find that:
- tan(37°) * cot(37°) = 1
This simplifies our expression to:
sin(37°) * cos(37°)
Using the double angle identity, we can further rewrite:
sin(37°) * cos(37°) = (1/2) * sin(2 * 37°) = (1/2) * sin(74°)
This is our expression in terms of sin(74°). However, if we’re seeking a numeric result, we can use the approximation:
sin(74°) ≈ 0.9613
Therefore:
sin(37°) * sin(53°) * tan(37°) * tan(53° ≈ (1/2) * 0.9613 ≈ 0.48065
If you would prefer to express this as a fraction, it can be approximated as:
≈ 24/50 = 12/25
Thus, the value of sin(37°) * sin(53°) * tan(37°) * tan(53° in terms of a fraction is approximately 12/25.