Warm-Up 1-13 Three gears in a machine are positioned relative to each other to form an isosceles right triangle as shown below. What is the distance between.

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Presentation transcript:

Warm-Up 1-13 Three gears in a machine are positioned relative to each other to form an isosceles right triangle as shown below. What is the distance between the center of the gears located at B and C? Leave your answer in simplest radical form.

Announcements  Test Next Thursday  Special Right Triangles  Trig  Online Homework 10-3 Due Sunday Night

Trigonometry Parts of a right triangle

When is it used?  Before the 16 th century trig was used to determine position of stars and planets  Here are some of the fields that use trigonometry TODAY  Astronomy  Navigation  Game Development  Engineering  Number Theory  Architecture  Pharmacy  Biology  Physics  Music Theory  And the list goes on…

Definitions  Reference Angle (θ) – the angle we are using  Hypotenuse - in a right triangle, it is the longest side of the triangle and it is located across from the right angle  Adjacent - The side that is adjacent, beside, next to, or touching θ  Opposite - The side opposite of θ

Label the sides of the triangles, given the reference angle. Look at the frist two triangles... How are they the same? How are they different?

 As the reference angle changes, the adjacent and opposite sides change, but the hypotenuse always stays the same

Three Trig Ratios  Sine  Abbreviated as sin  Cosine  Abbreviated as cos  Tangent  Abbreviated as tan

Trig Ratios(Sine, Cosine, Tangent)

Setting up trig ratios 1. Mark the angle you are using 2. Label the sides in relation to the reference angle (opp, adj, hyp) 3. Circle the two sides that you will be used in the trig ratio (use SOHCAHTOA) 4. Decide which side goes on top and which side goes on bottom 5. Write the fraction (and simplify!)

Practice

Homework  Online Homework due Sunday night

Classwork  Pg. 438 #1-9 just write the ratios, don’t solve for x.