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Published byGeorgije Damjanović Modified over 6 years ago
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pencil, red pen, highlighter, calculator, notebook
U8D6 Have out: Fill in the degrees and radian equivalent for all angles between 0° and 360° that are multiples of 30° and 45°. (Simplify all radians.) Bellwork: y Can you guess what your quiz will be on today??? Try to complete the bellwork WITHOUT looking at your notes. x When finished, work on Practice #1 of the worksheet. total:
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+1 each correct degree & radian
90˚ 120˚ y 60˚ 135˚ 45˚ 150˚ 30˚ 0˚ x 180˚ 360˚ 210˚ 330˚ 225˚ 315˚ 240˚ 300˚ 270˚ total:
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Finding and the Trig Equations
Practice #1: For each example, the given point is on the terminal side of . Complete the following: (iv) Label x, y, and r. (i) Plot the point. (v) Determine sin, cos, and tan. (ii) Show and α. (iii) Draw the reference triangle. (vi) Approximate .
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BTW, couldn’t we just have used special right triangles?
Practice #1: For each example, the given point is on the terminal side of . Complete the following: BTW, couldn’t we just have used special right triangles? Look at the ratios. (iv) Label x, y, and r. (i) Plot the point. (v) Determine sin, cos, and tan. (ii) Show and α. (iii) Draw the reference triangle. (vi) Approximate . 1) (–2, ) y α x
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Once again, couldn’t we just have used special right triangles?
Practice #1: For each example, the given point is on the terminal side of . Complete the following: Once again, couldn’t we just have used special right triangles? Look at the ratios. (iv) Label x, y, and r. (i) Plot the point. (v) Determine sin, cos, and tan. (ii) Show and α. (iii) Draw the reference triangle. (vi) Approximate . 2) (3, –3) y x α
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Practice #2: Draw in each quadrant
Practice #2: Draw in each quadrant. Show the reference triangle, α, and label x, y, and r. y y QI QII r r y y α x x x –x y y QIII QIV –x x x x α α –y –y r r
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> < > > < > < <
Practice #3: Insert the correct inequality symbol. (r > 0 for all quadrants) y y QI QII > < x __ 0 x __ 0 > y __ 0 > y __ 0 x x QIII y QIV y x x < > x __ 0 x __ 0 < < y __ 0 y __ 0
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ALL STUDENTS TAKE CALCULUS sin all tan cos
Conclusion: Given sin, cos, and tan, which are positive in each quadrant? y sin all II I x III IV There is a mnemonic to help you remember which functions are positive in each quadrant: tan cos ALL STUDENTS TAKE CALCULUS ________________________________________
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Practice #4: Answer the following:
1) If and , find cos, and tan, and . This means the terminal side of is in QIII. Our answer is in radians because the problem starts in radians. Be on the lookout for this scenario whenever you solve future problems. Make sure your calculator is in radian mode! y x α To find , pick the positive trig equation. (Our answer is in radians)
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2) If and , find sin, and tan, and .
This means the terminal side of is in QIV. y x α
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2) If and , find sin, and tan, and .
Look at the ∆. Anything “special”? It is a 30–60–90 ∆. y α is across from the long leg, so it is 60 . Recall: 60 = x α
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3) If tan = 1 and , find sin and (in radians).
In which quadrant is tangent positive and cosine negative? QIII y x α
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3) If tan = 1 and , find sin and (in radians).
Look at the ∆. It may be hard to notice, but is there anything “special”? It is an isosceles right ∆. y Therefore it is a 45–45–90 ∆. α is across from a leg, so it is 45 . Recall: 45 = x α
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4) If and tan = –2, find sin, and cos, and .
This means the terminal side of is in QII. y α x To find , pick the positive trig equation.
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Finish the practice worksheets
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