Sine, Cosine, Tangent (SOHCAHTOA) Calculator
This calculator is designed for students and professionals who need to quickly calculate the sine, cosine, and tangent of an angle using the SOHCAHTOA principle in trigonometry. Enter the angle and the length of the hypotenuse to get the results.
Results
Data Source and Methodology
All calculations are strictly based on standard trigonometric formulas. Please refer to authoritative sources like academic textbooks or verified online resources for the most accurate data.
The Formula Explained
Sine: \(\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}\)
Cosine: \(\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}\)
Tangent: \(\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\)
Glossary of Variables
- Angle (θ): The angle in degrees for which the trigonometric values are calculated.
- Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
- Opposite: The side opposite to the angle θ.
- Adjacent: The side adjacent to the angle θ.
How It Works: A Step-by-Step Example
For an angle of 30° and a hypotenuse of 10 units, the calculations would be:
- Sine: \( \sin(30) = 0.5 \times 10 = 5 \)
- Cosine: \( \cos(30) = 0.866 \times 10 = 8.66 \)
- Tangent: \( \tan(30) = 0.5774 \)
Frequently Asked Questions (FAQ)
What is SOHCAHTOA?
SOHCAHTOA is a mnemonic device to remember the definitions of sine, cosine, and tangent in trigonometry.
How do I use this calculator?
Simply enter the angle and the hypotenuse to compute the sine, cosine, and tangent values.
What units should I use for the hypotenuse?
Any consistent unit (e.g., meters, feet) can be used as long as it remains consistent throughout the calculation.
Can this calculator handle angles greater than 90 degrees?
No, it is specifically for right triangles where the angle is less than or equal to 90 degrees.
What should I do if I get unexpected results?
Ensure all inputs are correct and refer to standard trigonometric tables or resources for verification.
How accurate are the results?
The results are based on standard trigonometric calculations and are accurate to two decimal places.