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Trigonometric Ratios of Special Angles

Source: Glass Triangles - Philip Openshaw/iStock/Getty Images

Architecture

Triangles are important in construction because they cannot be deformed without breaking. 

Sources: Pyramids - ugurhan/E+/Getty Images; 

Glass Building - photovideostock/E+/Getty Images

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Lesson Goals

  • Recognize connections between the angles and the side lengths of a right isosceles triangle and between the angles and side lengths of an equilateral triangle.
  • Draw and find points on the terminal arm of angles in standard position with related acute angles of \(30^\circ\), \(45^\circ\), and \(60^\circ\).
  • Calculate exact values of the sine, cosine, and tangent ratios for angles related to \(30^\circ\), \(45^\circ\), \(60^\circ\), and \(90^\circ\).
  • Relate the points on the unit circle to the primary trigonometric ratios of angles in standard position.

Try This

Given \(\sin\left(\theta\right)=\cos\left(30^\circ\right),\:0^\circ\le\theta\le360^\circ\), determine all the possible measures of \(\theta\), without using a calculator.