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Degrees
Squared Values
sin²(θ):0.25
cos²(θ):0.75
tan²(θ):0.333
Using Formulas
sin²(θ) =
(1 - cos(2θ))/2 = 0.25
(1 - cos(2θ))/2 = 0.25
cos²(θ) =
(1 + cos(2θ))/2 = 0.75
(1 + cos(2θ))/2 = 0.75
Power Reducing Formulas:
sin²(θ) = (1 - cos(2θ)) / 2
cos²(θ) = (1 + cos(2θ)) / 2
tan²(θ) = (1 - cos(2θ)) / (1 + cos(2θ))
How to Use This Calculator
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View detailed breakdowns and explanations below.
📘 Power Reducing Formulas
sin²(θ) = (1 - cos(2θ)) / 2
cos²(θ) = (1 + cos(2θ)) / 2
tan²(θ) = (1 - cos(2θ)) / (1 + cos(2θ))
🎓 Higher Powers
For higher powers, apply the formulas repeatedly:
sin⁴(θ) = (sin²(θ))² = [(1 - cos(2θ))/2]²
sin⁴(θ) = (3 - 4cos(2θ) + cos(4θ)) / 8
💡 Derivation
These come from the double angle formulas:
cos(2θ) = 1 - 2sin²(θ)
Solving for sin²(θ): sin²(θ) = (1 - cos(2θ)) / 2
Solving for sin²(θ): sin²(θ) = (1 - cos(2θ)) / 2
🚀 Applications
- Integration: Essential for ∫sin²(x)dx and ∫cos²(x)dx
- Fourier Analysis: Converting to single frequency terms
- Physics: Energy calculations in oscillating systems
- Engineering: AC power analysis
⚡ Integration Example
∫sin²(x)dx = ∫(1 - cos(2x))/2 dx
= x/2 - sin(2x)/4 + C
= x/2 - sin(2x)/4 + C
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