Grade 10 Academic (MPM2D) Unit 5: Trigonometry Introduction to Trigonometry Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved

Trigonometry is a branch of mathematics that studies the relationship between the measures of the angles and the lengths of the sides in triangles. Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Investigation: Given the right triangle shown below Investigation: Given the right triangle shown below. A series of points B, D, F are selected along the base AH. Line segments BC, DE, FG are parallel to side HI with the points C, E, G on side AI. Fill in the table below. Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Investigation: Introduction to Trigonometry 6 15 FG = 9 AF = 22.5 HI = 10 AH = 25 Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Sine (Sin), COSINE (Cos), TANGENT (Tan): Opposite side Adjacent side Hypotenuse side Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1 Use a scientific calculator to find each value to 4 decimal places. a) sin 76° b) cos 6° c) tan 46° My Calculator procedures to evaluate trigonometry: Make sure your calculator is set to Degree Mode!! Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 2 Find the measure of each angle to the nearest degree “Inverse of Sine to 0.8988 is 64o” “Inverse of Cosine to 3/4 is 41o” “Inverse of Tangent to 2.1445 is 65o” My Calculator procedures to find the angle: Make sure your calculator is set to Degree Mode!! Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 3 Determine the value of x or y to the nearest centimetre. SOHCAHTOA Opposite & Hypotenuse Adjacent & Hypotenuse SINE COSINE Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 3 Determine the value of x or y to the nearest centimetre. SOHCAHTOA Opposite & Adjacent Opposite & Adjacent TANGENT TANGENT Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 4 Find the value of Sin , Cos  or Tan  and then calculate the measure of  to the nearest tenth degree. SOHCAHTOA Opposite & Hypotenuse Adjacent & Hypotenuse Opposite & Adjacent SINE COSINE TANGENT Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 5 a) Use the Pythagorean Theorem to calculate the unknown side Example 5 a) Use the Pythagorean Theorem to calculate the unknown side. b) For the angle marked ‘ ’and state the three primary trigonometric ratios. c) Find the value of to the nearest-tenth degree. (leave your answers in fractional form) SOHCAHTOA Opposite & Hypotenuse Missing Adjacent Let it be a or Three Primary Trigonometric Ratios in fraction form. or Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Example 6 Now go back to the investigation on Page 1 and determine the value for angle A. SOHCAHTOA Therefore 6 15 FG = 9 AF = 22.5 HI = 10 AH = 25 Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Summary: Sine (Sin), COSINE (Cos), TANGENT (Tan): Opposite side Adjacent side Hypotenuse side Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

Homework Work sheet: Introduction to Trigonometry Text: P. 496 # 4 - 6 Check the website for updates Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved

End of lesson Introduction to Trigonometry © 2017 E. Choi – MPM2D - All Rights Reserved