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Introduction to trigonometry

This section covers the basics of trigonometry, specifically focusing on calculating the lengths of sides in right triangles using trigonometric ratios. By introducing sine, cosine, and tangent functions, students will learn to determine the side lengths given one side and one acute angle. With practical examples and calculator evaluations, learners will explore how to use trigonometric definitions effectively. The use of mnemonics like "SohCahToa" will aid in remembering ratios while developing problem-solving skills through assignments and exercises.

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Introduction to trigonometry

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  1. Section 8.2 Introduction to trigonometry “triAngle Measures” Objective: To find the length of a side of a right triangle, given one side and one acute angle.

  2. Recall… Make a guess…. 60° Find the value of x. 10 x 55° Now make a conjecture about the value of y in the figure. 10 y Trigonometry will help us find the length of a side of a right triangle when we are given only one side and one acute angle.

  3. Evaluate each function on a calculator. a. sin 30° c. tan 30 ° b. cos 30 ° 0.87 0.58 0.5 What do these numbers mean? Where do they come from?

  4. Trig definitions 10 5 30 sin (angle) = tan (angle) = cos (angle) =

  5. Trig definitions 6 3 30 sin (angle) = tan (angle) = cos (angle) =

  6. So when I type sin 30 into my calculator, it is telling me that the RATIO of the leg opposite the 30 angle and the hypotenuse is or 0.5. So how am I going to remember this?

  7. D J A C E N T P P O S I T E I N E O S I N E Y P O T E N U S E Y P O T E N U S E A N G E N T P P O S I T E D J A C E N T SohCahToa Aaaahh!

  8. Handbook page 18

  9. Here’s what you need to be able to do: • Given the right triangle shown, state the ratio for the sine, cosine and tangent of A and B. B 6 10 A

  10. 18 37° 2. Find the value of x in each triangle. a. b. x 43° x 4.1

  11. Now use trigonometry to find the actual value of y, rounded to the nearest hundredth. 55° 10 y

  12. Assignment WS: Intro to Trig Ratios: 1-19

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