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precalc b: trigonometry > midterm exam study > Flashcards

midterm exam study Flashcards

study and memorize all key and fundamental concepts introduced in chapters 5 and 6.

1
Q

5.1: angles

what rotation generates a positive degree measure? what rotation generates a negative degree measure?

A

a counter-clockwise rotation generates positive and a clockwise rotation generates negative measure.

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2
Q

5.1: angles

(blank) has a sum of 90 deg.

A

complement

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3
Q

5.1: angles

(blank) has a sum of 180 deg.

A

supplement

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4
Q

5.1: angles

how many degrees are measured in 1 revolution?

A

360 degrees

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5
Q

5.1: angles

how many degrees are measured in 1 hour?

A

1 degree per 60 minutes (1 hour)

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6
Q

5.1: angles

convert this to decimal degrees to the nearest thousandth.
105 deg 20 ‘ 32 “

A

approx. 105.342 deg

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7
Q

5.1: angles

define standard position.

A

when an angle has a vertex at the origin and its initial side lies on the positive x-axis.

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8
Q

5.1: angles

define quadrantal angles.

A

angles that are in standard position whose terminal side lie on the x or y-axis, such as 90 deg, 180 deg, 270 deg, etc.

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9
Q

5.1: angles

what are coterminal angles?

A

angles with measures 60 deg and 420 deg that have the same intial side and the same terminal side BUT different amounts of rotation. their measures differ by a multiple of 90 deg.

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10
Q

5.1: angles

find the angle of least positive measure that is coterminal with the angle: 1106 deg.

A

26 deg in Quartile 1.

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11
Q

5.1: angles

find the angle of least positive measure that is coterminal with the angle: -603 deg.

A

117 deg in Quartile 2.

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12
Q

5.2: trigonometric functions

define the six trigonometric functions (of theta).

A
  1. sin = y/r
  2. cos = x/r
  3. tan = y/x
  4. csc = r/y
  5. sec = r/x
  6. cot = x/y
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13
Q

5.2: trigonometric functions

how do you find “R” (also known as the hypotenuse)?

A

by using pythagorean theorem and solving. otherwise, SQRT[x^2 + y^2]

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14
Q

5.2: trigonometric functions

what are the reciprocol identities for all 6 trigonometric functions?

A
  1. sin = 1/csc
  2. cos = 1/sec
  3. tan = 1/cot
  4. csc = 1/sin
  5. sec = 1/cos
  6. cot = 1/tan
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15
Q

5.2: trigonometric functions

which functions are positive in q1?

A

[all] functions

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16
Q

5.2: trigonometric functions

which functions are positive in q2?

A

(strippers) sin and csc

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17
Q

5.2: trigonometric functions

which functions are positive in q3?

A

(take) tan and cotan

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18
Q

5.2: trigonometric functions

which functions are positive in q4?

A

(cash) cos and sec

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19
Q

5.2: trigonometric functions

identify the quadrant or possible quadrants of the angle theta (@) that satisfies given conditions: tan@ > 0, csc@ < 0

A

theta is an element of quadrant 3.

20
Q

5.2: trigonometric functions

what are the ranges of sin@ and cos@?

A

-1 less than/equal to Y less than/equal to 1.
[-1, 1]

21
Q

5.2: trigonometric functions

what are the ranges of tan@ and cot@?

A

(neg infinity, pos infinity)

22
Q

5.2: trigonometric functions

what are the ranges of sec@ and csc@?

A

(-neg infinity, -1] U [1, infinity)

23
Q

5.2: trigonometric functions

based on the ranges of the trig functions, determine whether cot@ = -0.999 is possible or impossible.

24
Q

5.2: trigonometric functions

based on the ranges of the trig functions, determine whether cos@ = -1.7 is possible or impossible.

A

impossible

25
Q

5.2: trigonometric functions

what are the three pythagorean identities? (of theta)

A
  1. sin^2 + cos^2 = 1
  2. tan ^2 + 1 = sec ^2
  3. 1 + cot^2 = csc^2
26
Q

5.2: trigonometric functions

what are the two quotient identities? (of theta)

A
  1. sin/cos = tan
  2. cos/sin = cot
27
Q

5.3: trigonometric function values and angle measures

what are the right-triangle based definitions of the six trig functions?

(think SOHCAHTOA)

A
  1. sin a = opp/hyp
  2. cos a = adj/hyp
  3. tan a = opp/adj
  4. csc a = hyp/opp
  5. sec a = hyp/adj
  6. cotan a = adj/opp
28
Q

5.3: trigonometric function values and angle measures

define the cofunction identities for the six trig functions.

A
  1. sin a = cos(90 - A)
  2. cos a = sin(90 - A)
  3. sec a = csc(90 - A)
  4. csc a = (90 - A)
  5. tan a = cot(90 - A)
  6. cot a = tan(90 - A)
29
Q

5.3: trigonometric function values and angle measures

cofunction values of complementary angles are (blank)

30
Q

5.3: trigonometric function values and angle measures

what are the three types of triangles?

A

equilaterial: all sides same
isosoles: two sides same
scalene: no sides same

31
Q

5.3: trigonometric function values and angle measures

what are the values of the six trig functions for 30 deg?

function values of special angles chart

A

view https://www.mathwords.com/t/t_assets/t80.gif

32
Q

5.3: trigonometric function values and angle measures

what are the values of the six trig functions for 45 deg?

A

view https://www.mathwords.com/t/t_assets/t80.gif

33
Q

5.3: trigonometric function values and angle measures

what are the values of the six trig functions for 60?

A

view https://www.mathwords.com/t/t_assets/t80.gif

34
Q

5.3: trigonometric function values and angle measures

what are the values of the six trig functions for 90?

A

view https://www.mathwords.com/t/t_assets/t80.gif

35
Q

5.3: trigonometric function values and angle measures

what is a reference angle?

A

for angle theta (@), a reference angle is the positive acute angle made by the terminal side of angle @ and the x-axis. written @’.

36
Q

5.3: trigonometric function values and angle measures

the reference angle is always found in reference to the (blank)

A

x-axis.
@’ = @ - 180 <-> @ = 180 + @’

37
Q

5.3: trigonometric function values and angle measures

what are the 4 steps to finding trig function values for any nonquadrantal angle?

A
  1. if @ > 360, or if @ < 0, find a coterminal angle by subtracting/adding 360 as many times as neede to get an angle greater than 0 but less than 360
  2. find the ref angle @’
  3. find the trig function value for ref angle @’
  4. determine correct signs for the values found
38
Q

5.4: solutions and applications of right triangles

what are the significant digits for angles in degrees?

39
Q

5.4: solutions and applications of right triangles

what are the significant digits for angles in ten minutes/nearest tenth of a degree?

40
Q

5.4: solutions and applications of right triangles

what are the significant digits for angles in minutes/nearest hundreth of a degree?

41
Q

5.4: solutions and applications of right triangles

what are the significant digits for angles in ten seconds/nearest thousandth of a degree?

42
Q

5.4: solutions and applications of right triangles

an angle of elevation opens …

A

facing upwards

43
Q

5.4: solutions and applications of right triangles

an angle of depression opens …

A

facing downwards

44
Q

5.4: solutions and applications of right triangles

both the angle of elevation and the angle of depression are measured between the line of sight and a (blank)

45
Q

5.4: solutions and applications of right triangles

what is method 1 of expressing bearing?

A

(when one angle is given) bearing is measured in a clockwise direction from due north

46
Q

5.4: solutions and applications of right triangles

what is method 2 of expressing bearing?

A

start with north-south line and use an acute angle to show the direction, east or west, from this line

precalc b: trigonometry (1 decks)

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