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Introduction to Trigonometry

Introduction to Trigonometry. Honors Geometry December 5, 2016. As you know, all the triangles below are similar. Why?. 3 5 4 6 10 9 15 8

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Introduction to Trigonometry

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  1. Introduction to Trigonometry Honors Geometry December 5, 2016

  2. As you know, all the triangles below are similar. Why? 3 5 4 6 10 9 15 8 12

  3. As you know, all the triangles below are similar. Why? 3 5 4 6 10 9 15 8 12 They are similar because of the SSS ~ postulate.

  4. This means that corresponding sides of these triangles are proportional.Let’s look at the smallest angle in each of these triangles and check this property! But what angle will be the smallest?

  5. The angle opposite the shortest side will always be the smallest angle in a triangle. Using this knowledge, let’s call the smallest angle in each triangle  (the Greek letter theta), and, with reference to , check out the ratio of the length of the side opposite of  to the length of the hypotenuse of the triangle. (We call this ratio sin .)

  6. Sin θ = 3 5 4 6 10 9 15 8 12 θ θ θ

  7. As you can see, the sine of  is the same each time, since the angle  is the same each time.

  8. There are two other relationships that are important in trigonometry as well. In terms of any acute angle  in a right triangle, they are:

  9. You need to know these! sine  or sin  = cosine  or cos  = tangent  or tan  =

  10. Find the sine, cosine, and tangent of A in the triangle below. A 13 B 12 C

  11. Find the sine, cosine, and tangent of A in the triangle below. A 13 5 B 12 C Sin A = Cos A = Tan A =

  12. Find the sine, cosine, and tangent of B in the triangle below. A 13 B 12 C Sin B = Cos B = Tan B =

  13. Let’s find the calculator connections. Draw a 30º-60º-90º to help you find sin 30º. Now use your calculator to find sin 30º. (Be sure your mode is in degrees.) So… What is sin 45º? What is cos 27º? What is tan 62º? 0.7071 .8910 1.881

  14. Can the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. R P Q

  15. Can the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. R P 16 Q 35

  16. Can the calculator help us solve this problem? In triangle PQR, mP = 90º, and mQ = 35º. If PQ = 16, find the lengths of the other two sides. R P 16 Q 35

  17. What are the implications??? • The angle of inclination of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite actually flying?

  18. What are the implications??? • The angle of inclination of a kite with respect to the ground is 79º. If 100’ of string is holding the kite to the ground, how high is the kite actually flying? 100’ 79º

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