Special Angles
- A unit circle can be used to find the trigonometric ratios of angles greater than 90 degrees.
special_angles.doc | |
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Homework Questions: MHR Functions 11: 4.1: # 3, 5, 6, 10, 11, 12
Co-Terminal and Related Angles
- For any given sine, cosine or tangent ratio, there are two distinct angles between 0 degrees and 360 degrees which will have this same sine, cosine, or tangent ratio
- Pairs of related angles can be found using the coordinates of the endpoints of their terminal arms. SUe a reference angle in the first quadrant
- Co-Terminal angles are angles with the same terminal arm. They can be positive or negative.
coterminal_and_related_angles_p1.pdf | |
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coterminal_and_related_angles_p2.pdf | |
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section_4_2_question_11_and_12.pdf | |
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Homework Questions: MHR Functions 11: 4.2: # 1 - 12
Reciprocal Trigonometric Identities
- The reciprocal of sine is cosecant
- The reciprocal of cosine is secant
- The reciprocal of tangent is cotangent
Homework Questions: MHR Functions 11: 4.3 # 2 - 13
reciprocal_trigonometric_identities_filled_out.doc | |
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Solving Problems in Two Dimensions. The Ambiguous Case of the Sine Law
- When considering a non right angle triangle given the SSA case where two sides are given and the non-included angle; it is possible that there is one, two, or zero triangles possible with the given measurement
Homework Questions:
- MHR Functions 11: 4.4: #3, 4, 6, 7, 8.
- McGraw Hill Mathematics 11. 4.4 Pg 308 - 309 # 2, 4, 5
the_sine_law.doc | |
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the_cosine_law.doc | |
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the_ambiguous_case_of_the_sine_law.doc | |
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2d_problems_notes_p1.pdf | |
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2d_problems_notes_p2.pdf | |
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2d_problems_notes_p3.pdf | |
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Problems in 3 Dimensions
- Three-dimensional problems involving triangles can be solved using one or more of the following: the Pythagorean theorem, the six trigonometric ratios, the sine law, and the cosine law.
- The method chosen to solve a triangle depends on the known information.
Homework Questions:
- MHR Functions 11: 4.5: # 1, 2, 3, 6, 7
solving_problems_in_3_dimensions_filled_out.doc | |
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Trigonometric Identities
- An identity is an equation where the left side of the equation equals the right side of the equation for all values of the variable defined.
- Proving a trigonometric identity involves re-writing each side of the equation in a simpler form so that you may prove that the right side can be simplified to look exactly like the right side.
- When proving trigonometric identities there are 3 key identities to remember: The Quotient Identity, the Pythagorean Identity, and the Reciprocal Trig Identities.
Homework Questions:
- MHR Functions 11: 4.6: # 3 - 9, 12, 13
- McGraw Hill Mathematics 11: 5.7: pg 398 - 399 # 2, 3, 4