midterm exam study

Question 1

5.1: angles

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

Answer 1

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

Question 2

5.1: angles

(blank) has a sum of 90 deg.

Answer 2

complement

Question 3

5.1: angles

(blank) has a sum of 180 deg.

Answer 3

supplement

Question 4

5.1: angles

how many degrees are measured in 1 revolution?

Answer 4

360 degrees

Question 5

5.1: angles

how many degrees are measured in 1 hour?

Answer 5

1 degree per 60 minutes (1 hour)

Question 6

5.1: angles

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

Answer 6

approx. 105.342 deg

Question 7

5.1: angles

define standard position.

Answer 7

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

Question 8

5.1: angles

define quadrantal angles.

Answer 8

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.

Question 9

5.1: angles

what are coterminal angles?

Answer 9

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.

Question 10

5.1: angles

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

Answer 10

26 deg in Quartile 1.

Question 11

5.1: angles

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

Answer 11

117 deg in Quartile 2.

Question 12

5.2: trigonometric functions

define the six trigonometric functions (of theta).

Answer 12

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

Question 13

5.2: trigonometric functions

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

Answer 13

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

Question 14

5.2: trigonometric functions

what are the reciprocol identities for all 6 trigonometric functions?

Answer 14

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

Question 15

5.2: trigonometric functions

which functions are positive in q1?

Answer 15

[all] functions

Question 16

5.2: trigonometric functions

which functions are positive in q2?

Answer 16

(strippers) sin and csc

Question 17

5.2: trigonometric functions

which functions are positive in q3?

Answer 17

(take) tan and cotan

Question 18

5.2: trigonometric functions

which functions are positive in q4?

Answer 18

(cash) cos and sec

Question 19

5.2: trigonometric functions

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

Answer 19

theta is an element of quadrant 3.

Question 20

5.2: trigonometric functions

what are the ranges of sin@ and cos@?

Answer 20

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

Question 21

5.2: trigonometric functions

what are the ranges of tan@ and cot@?

Answer 21

(neg infinity, pos infinity)

Question 22

5.2: trigonometric functions

what are the ranges of sec@ and csc@?

Answer 22

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

Question 23

5.2: trigonometric functions

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

Answer 23

possible

Question 24

5.2: trigonometric functions

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

Answer 24

impossible

Question 25

# 5.2: trigonometric functions what are the three pythagorean identities? (of theta)

Answer 25

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

Question 26

# 5.2: trigonometric functions what are the two quotient identities? (of theta)

Answer 26

1. sin/cos = tan 2. cos/sin = cot

Question 27

# 5.3: trigonometric function values and angle measures what are the right-triangle based definitions of the six trig functions? | (think SOHCAHTOA)

Answer 27

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

Question 28

# 5.3: trigonometric function values and angle measures define the cofunction identities for the six trig functions.

Answer 28

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)

Question 29

# 5.3: trigonometric function values and angle measures cofunction values of complementary angles are (blank)

Answer 29

equal

Question 30

# 5.3: trigonometric function values and angle measures what are the three types of triangles?

Answer 30

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

Question 31

# 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

Answer 31

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

Question 32

# 5.3: trigonometric function values and angle measures what are the values of the six trig functions for 45 deg?

Answer 32

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

Question 33

# 5.3: trigonometric function values and angle measures what are the values of the six trig functions for 60?

Answer 33

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

Question 34

# 5.3: trigonometric function values and angle measures what are the values of the six trig functions for 90?

Answer 34

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

Question 35

# 5.3: trigonometric function values and angle measures what is a reference angle?

Answer 35

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

Question 36

# 5.3: trigonometric function values and angle measures the reference angle is always found in reference to the (blank)

Answer 36

x-axis. @' = @ - 180 <-> @ = 180 + @'

Question 37

# 5.3: trigonometric function values and angle measures what are the 4 steps to finding trig function values for any nonquadrantal angle?

Answer 37

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

Question 38

# 5.4: solutions and applications of right triangles what are the significant digits for angles in degrees?

Answer 38

two

Question 39

# 5.4: solutions and applications of right triangles what are the significant digits for angles in ten minutes/nearest tenth of a degree?

Answer 39

three

Question 40

# 5.4: solutions and applications of right triangles what are the significant digits for angles in minutes/nearest hundreth of a degree?

Answer 40

four

Question 41

# 5.4: solutions and applications of right triangles what are the significant digits for angles in ten seconds/nearest thousandth of a degree?

Answer 41

five

Question 42

# 5.4: solutions and applications of right triangles an angle of elevation opens ...

Answer 42

facing upwards

Question 43

# 5.4: solutions and applications of right triangles an angle of depression opens ...

Answer 43

facing downwards

Question 44

# 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)

Answer 44

ray

Question 45

# 5.4: solutions and applications of right triangles what is method 1 of expressing bearing?

Answer 45

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

Question 46

# 5.4: solutions and applications of right triangles what is method 2 of expressing bearing?

Answer 46

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