 # SPECIAL USING TRIANGLES Computing the Values of Trig Functions of Acute Angles.

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SPECIAL USING TRIANGLES Computing the Values of Trig Functions of Acute Angles

The 45-45-90 Triangle In a 45-45-90 triangle the sides are in a ratio of 1- 1- This means I can build a triangle with these lengths for sides (or any multiple of these lengths) 45° 90° 1 1 We can then find the six trig functions of 45° using this triangle. rationalized Can "flip" these to get other 3 trig functions

You are expected to know exact values for trig functions of 45°. You can get them by drawing the triangle and using sides. 45° 90° 1 1 What is the radian equivalent of 45°? You also know all the trig functions for  /4 then. reciprocal of cos so h over a

The 30-60-90 Triangle In a 30-60-90 triangle the sides are in a ratio of 1- - 2 This means I can build a triangle with these lengths for sides 60° 30° 90° 2 1 We can then find the six trig functions of 30°or 60° using this triangle. Be sure to locate the angle you want before you find opposite or adjacent side opp 60° side opp 30° side opp 90° I used the triangle and did adjacent over hypotenuse of the 60° to get this but it is the cofunction of sine so this shows again that cofunctions of complementary angles are equal.

What this means is that if you memorize the special triangles, then you can find all of the trig functions of 45°, 30°, and 60° which are common ones you need to know. You also can find the radian equivalents of these angles. When directions say "Find the exact value", you must know these values not a decimal approximation that your calculator gives you.

Using a Calculator to Find Values of Trig Functions If we wanted sin 38° we could not use the previous methods to find it because we don't know the lengths of sides of a triangle with a 38° angle. We will then use our calculator to approximate the value. You can simply use the sin button on the calculator followed by (38) to find the sin 38° A word to the wise: Always make sure your calculator is in the right mode for the type of angle you have (degrees or radians)

Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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