Trigonometry!

What is it? The study of the relationships between the sides and angles of right triangles

Okay….and that means? Think about the Special Right Triangles we learned about. The ratio, or relationship between their side lengths always stayed the same. Why did they stay the same? AA SIMILARITY!

How did this come about? Early mathematicians noticed these relationships and took the time to record the ratios for each angle measurement. To make this process faster to look up, they create the names sine, cosine and tangent for the ratios of different sides and eventually, to streamline use with calculators and computers we created functions by these names that automatically store those ratios.

Look at the 4 triangles below. What is the ratio of the side lengths for 31 degrees? What is the value of x?

What is the ratio for 42 degrees? What is the value of y?

Solving Trig Questions Most important part….DRAW the right picture and label it correctly! Step 1 – Draw and label sides/angles of triangle if necessary Step 2 – Choose and angle Step 3 – Label opposite, adjacent and hypotenuse Step 4 – Use sine, cosine or tangent to calculate!

Show your Understanding! On a piece of computer paper draw two congruent right triangles. Label the sides and vertices Show what the trigonometric functions would be for each angle Color coordinate the trig functions with their angles. Color coordinate the sides of the triangles with their labels in the trigonometric functions