30-60-90 Triangles - Special Right Triangle Trigonometry
The Organic Chemistry Tutor・3 minutes read
In a 30-60-90 triangle, specific side lengths correspond to trigonometric functions of 30 and 60 degrees, simplifying calculations without the need to memorize the unit circle. The ratios of sine, cosine, secant, tangent, and cotangent for each angle can be determined using the defined side lengths in the triangle.
Insights
- The side lengths in a 30-60-90 triangle have specific relationships where the side opposite the 30-degree angle is 1, the side opposite the 60-degree angle is 1 times the square root of 3, and the side opposite the 90-degree angle is 2, allowing for the calculation of trigonometric functions based on these ratios.
- Trigonometric functions like sine, cosine, secant, tangent, and cotangent for 30 and 60-degree angles in a 30-60-90 triangle have precise values that can be determined using the side lengths, providing a method to compute these functions without the need to memorize the unit circle.
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Recent questions
What are the side lengths of a 30-60-90 triangle?
1, square root of 3, 2
What are the trigonometric functions for a 30-degree angle in a 30-60-90 triangle?
Sine: 1/2, Cosine: sqrt(3)/2, Secant: 2sqrt(3)/3, Tangent: sqrt(3)/3, Cotangent: sqrt(3)
What are the trigonometric functions for a 60-degree angle in a 30-60-90 triangle?
Sine: sqrt(3)/2, Cosine: 1/2, Secant: 2, Tangent: sqrt(3), Cotangent: sqrt(3)/3
How can trigonometric functions be calculated in a 30-60-90 triangle?
Using specific ratios based on side lengths
What is the significance of the side lengths in a 30-60-90 triangle?
Determine trigonometric functions for specific angles
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Summary
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Trigonometric Functions in 30-60-90 Triangle
- In a 30-60-90 triangle, the side opposite the 30-degree angle is 1, the side opposite the 60-degree angle is 1 times the square root of 3, and the side opposite the 90-degree angle is 2. When finding trigonometric functions like sine, cosine, secant, tangent, and cotangent of 30 and 60 degrees in this triangle, specific ratios can be calculated using these side lengths.
- For a 30-degree angle, sine is 1/2, cosine is square root of 3 over 2, secant is 2 square root 3 over 3, tangent is square root 3 over 3, and cotangent is square root 3. For a 60-degree angle, sine is square root of 3 over 2, cosine is 1/2, secant is 2, tangent is square root 3, and cotangent is square root 3 over 3, providing a method to evaluate trigonometric functions without needing to memorize the unit circle.
