query: How were the values of this trigonmetric ratio determined?
positive_passages.docid: 155148
positive_passages.text: Why is $\sin 30^\circ=\frac{1}{2}$
negative_passages.docid: 149686
negative_passages.text: Combinatorics and trigonometry identity
negative_passages.docid: 3098
negative_passages.text: How are first digits of $\pi$ found?
negative_passages.docid: 33791
negative_passages.text: Is it generally true that $\arcsin \theta + \arccos \theta = \frac{\pi}{2}$?
negative_passages.docid: 18546
negative_passages.text: Geometric intuition for $\pi /4 = 1 - 1/3 + 1/5 - \cdots$?
negative_passages.docid: 55179
negative_passages.text: How to find the exact value of $ \cos(36^\circ) $?
negative_passages.docid: 126040
negative_passages.text: Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
negative_passages.docid: 83359
negative_passages.text: Complex number identity by trigonometry
negative_passages.docid: 109171
negative_passages.text: How to evaluate this trigonometric limit?
negative_passages.docid: 23518
negative_passages.text: How are the Lagrange points determined?
negative_passages.docid: 73445
negative_passages.text: Is Pythagoras the only relation to hold between $\cos$ and $\sin$?
negative_passages.docid: 41340
negative_passages.text: Why do clocks measure arc-length?
negative_passages.docid: 111968
negative_passages.text: Uses of the 'Golden Ratio'
negative_passages.docid: 28582
negative_passages.text: How to find points of tangency on an ellipse?
negative_passages.docid: 40869
negative_passages.text: Solving Trigonometric Limits
negative_passages.docid: 135543
negative_passages.text: Proof of Angles going beyond 90 degrees in Trigonometry
negative_passages.docid: 83290
negative_passages.text: How is the value of $\pi$ ( Pi ) actually calculated?