Precalculus 12/4/2014 DO NOW/Bellwork 1)Convert to radians 220º AGENDA o Do Now/Bellwork o HW questions o SOHCAHTOA and its applications Essential Question:

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Right Triangle Trigonometry

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Presentation transcript:

Precalculus 12/4/2014 DO NOW/Bellwork 1)Convert to radians 220º AGENDA o Do Now/Bellwork o HW questions o SOHCAHTOA and its applications Essential Question: How can the study of trigonometry be used in the real world? HOMEWORK: pg even Objectives: You will be able to analyze and solve problems using trig and inverse trig graphs.

Triangles! SOHCAHTOA sincos tan opposite Hypotenuse adjacent Hypotenuse Fill in the unit circle using exact values of trig and radian measure

Other Trig Functions to know Cosecant Secant Cotangent Fill in the unit circle using exact values of trig and radian measure

SOHCAHTOA

Special triangles (isosceles right triangle) (comes from an equilateral triangle )

Evaluating trig functions of 45º Find the values of all six trig. functions for an angle of 45º Size of triangle doesn’t matter, we set lengths of 2 equal legs at 1.

Evaluating trig functions of 30º Find the values of all six trig. functions for an angle of 30º Size of triangle doesn’t matter, split the altitude into 2 congruent triangles each with a leg of 1 and hypotenuse of 2.

Now do the same for 60º Find the values for all 6 trig functions for an angle of 60º. Compare the six function values for 60º with the 6 function values for 30º. What do you notice? We will eventually learn a rule that relates trigonometric functions of any angle with trigonometric functions of the complementary angle. (complementary because they add up to 90º) Based on this exploration, can you predict what that rule will be?

Answers Fill in the unit circle using exact values of trig and radian measure

Using a trig ratio to find all the other trig ratios sin Fill in the unit circle using exact values of trig and radian measure sin

Solving Problem with the Cosine Ratio hypotenuse adjacent opposite Find the adjacent side 36 ft

Using a Calculator On the calculator enter the hit the “2nd” button and then the “Sin” button. On a graphics calculators you will enter it just like it reads in the equation. 8 3 The number should be displayed. This is the angle that has a Sin value of Then you can calculate the angle value. Then, that means