Trigonometry: the study of how sides and angles of a triangle are related to each other
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a² + b² = c²
leg² + leg² = hypotenuse²
Primary Trigonometric Ratios | Secondary Trigonometric Ratios |
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==sinθ = O/H== | ==cscθ = H/O== |
@@cosθ = A/H@@ | @@secθ = H/A@@ |
tanθ = O/A | cotθ = A/O |
cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ
→ you can solve by using the reciprocal when facing a secondary trig ratio
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Most often seen in word problems
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The angle between the line of sight and the horizontal from the eye
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The angle when looking down, between the line of sight and the horizontal from the eye
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You may not use decimals here, as that is not the true exact value
Used to find the exact values for 45º, 45º isosceles triangles and for 60º, 30º triangles (remember: sum of a triangle’s angles must be 180º)
Remember that you must rationalize your final answer
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The angle, θ, is known as the principal angle (PA)→ its value can fall between 0º and 360º depending on which quadrant the terminal arm is in
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The related acute angle (RAA) %%sits between the terminal arm and the x axis%% in any quadrant
In each quadrant, the given ratio (indicated in the letter) is positive, and in all other quadrants it is negative
Apply the formula used to find the circumference of a circle to SOH CAH TOA
Adapted SOH CAH TOA becomes:
Use the Pythagorean theorem (adapted to circle, same formula → x² + y² = r² ) to get the missing value
Use a primary trig ratio to find the RAA:
ratio⁻¹(side O, A, H depending on question/side O, A, H depending on question) = RAA
Use RAA to calculate PA (dependent on the quad, Recall: RAA and PA in Each Quadrant graphic above)
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For triangle ABC:
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