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Trigonometry and Geometry

The concept of reference angles will be used to find equivalent ratios for sine, cosine, and tangent in different quadrants.
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The exact value of the trigonometric ratios for 0°, 30°, 45°, 60°, and 90° will be discovered by analyzing the unit circle using special triangles.
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The ratios of the 45-45-90 triangle will be derived using the Pythagorean Theorem. The properties of the special triangles can then be applied to the trigonometric ratios of sine and cosine.
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The ratios of the 30-60-90 triangle will be derived using the Pythagorean Theorem. The ratios when the be applied to quickly find the side lengths of any 30-60-90 triangle.
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Basic geometry and mathematics are used in this problem set to explain varying properties of an ascending series of n-dimensional units.
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The concept of surface area is explored through the iterative processes in creating a Menger sponge.
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Varying lines and diagonals in cubes and tetrahedral are examined and solved for in this series of problems.
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