Slide show on an intro to trigonometry

1. Right Triangle Trigonometry Hypotenuse Opposite 𝜃 Adjacent

2. Review Sides and Angles of a Right Triangle Theta= angle in a right triangle (𝜃) Opposite= side opposite of angle Adjacent= side next to angle Hypotenuse= long side of right triangle Anybody need to see a picture?

3. 3 Functions for Right Triangles Sine (sin) Cosine (cos) Tangent (tan)

4. What are these Functions Used For? Shows relationships between sides and angles Find the length of missing side: When given an angle and side Find measure of the missing angle When given the length of sides

5. Sine Sine = Opposite/Hypotenuse Hypotenuse Opposite 𝜃

6. Cosine Cos = Adjacent/Hypotenuse Type equation here. Hypotenuse 𝜃 Adjacent

7. Tangent Tan = Opposite/Adjacent Opposite 𝜃 Adjacent

8. Way to Remember Which Sides to Divide SOHCAHTOA SOH Sin = Opposite/Hypotenuse CAH Cos = Adjacent/Hypotenuse TOA Tan = Opposite/Adjacent

9. Example 1 I will do this one with you Recall the 45°- 45°- 90°- right triangle Find sin, cos, tan of 45° angle in the bottom right Type equation here. 45° √2 1 45° 90° 1

10. Example 1 continued Sin(θ) = opposite/hypotenuse Sin(45°) = 1/√2 ≈ .707 Cos(θ) = adjacent/hypotenuse Cos(45°) = 1/√2 ≈ .707 Tan(θ) = opposite/adjacent Tan(45°) = 1/1 = 1

11. Example 2 Work in groups of 3 Find sin, cos, tan of 70° angle Round your answers to the nearest hundredth 5.5 5.1 70° 1.9

12. Example 2 continued Sin(θ) = opposite/hypotenuse Sin(70°) = 5.1/5.5 ≈ .93 Check answer using calculator Cos(θ) = adjacent/hypotenuse Cos(70°) = 1.9/5.5 ≈ .35 Calculator Tan(θ) = opposite/adjacent Tan(70°) = 5.1/1.9 ≈ 2.69 Calculator

13. What Happens When…? Find the length of x What trig function do we have? Sin(63°) = x/7 Multiply 7 by sin(63°) to get answer Use your calculator to round to nearest tenth Answer: x ≈ 6.2 7 x 63°

14. What about…? Find the measure of the angle Round to the nearest degree What trig function is shown here? Cosine 10 𝜃 4

15. What about…? continued Set up the function so it can be solved Cos (𝜃) = 4/10 To solve for 𝜃: Need to get 𝜃 by itself On your calculators: Hit the 2nd button on your calculator Push the cos button 2nd button gives you inverse cosine (cos-1) So cos-1(4/10) is about 66 degrees Any questions?

16. What Did We Learn Today? Reviewed angles, sides of right triangle What 𝜃 is Sin, cos, and tan What they are How they are used REMEMBER SOHCAHTOA!! Special cases Drawings and symbols used by Microsoft Arts