1. Grade 10 Academic (MPM2D) Unit 5: Trigonometry Introduction to Trigonometry
Mr. Choi
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2. 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
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3. 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
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4. Investigation: Introduction to Trigonometry 6 15 FG = 9 AF = 22.5
HI = 10
AH = 25
Introduction to Trigonometry
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5. Sine (Sin), COSINE (Cos), TANGENT (Tan):
Opposite side
Adjacent side
Hypotenuse side
Introduction to Trigonometry
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6. 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
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7. Example 2 Find the measure of each angle to the nearest degree
“Inverse of Sine to
is 64o”
“Inverse of Cosine to
3/4 is 41o”
“Inverse of Tangent to
is 65o”
My Calculator procedures to find the angle:
Make sure your calculator is set to Degree Mode!!
Introduction to Trigonometry
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8. Example 3 Determine the value of x or y to the nearest centimetre.
SOHCAHTOA
Opposite & Hypotenuse
Adjacent & Hypotenuse
SINE
COSINE
Introduction to Trigonometry
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9. Example 3 Determine the value of x or y to the nearest centimetre.
SOHCAHTOA
Opposite & Adjacent
Opposite & Adjacent
TANGENT
TANGENT
Introduction to Trigonometry
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10. 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

11. 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

12. 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

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

14. Homework
Work sheet: Introduction to Trigonometry Text: P. 496 # Check the website for updates
Introduction to Trigonometry
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15. End of lesson Introduction to Trigonometry
© 2017 E. Choi – MPM2D - All Rights Reserved