Chapter 6: The Trig Tango

Question 1

what is the inverse trig function of

sin30° = 1/2

Answer 1

sin⁻¹1/2 = 30°

Question 2

• graph of the tangent function
• what is the period of the tangent function

Answer 2

Question 3

• graph of sin and cos
• period of sin and cos is

Answer 3

Question 4

period of periodic function

Answer 4

the length of one of its cycles

Question 5

sine, cosine, and tangent (and their reciprocals) are periodic functions, which means

Answer 5

their graphs contain a basic shape that repeats over and over indefinitely to the left and right

Question 6

Remembering how to draw unit circle w/16 special angles

Quadrant 1: (x, y), (cosine, sine) coordinates

Answer 6

Step 1:

• Cosine: count down from 4 to 0
• Sine: count up from 1 to 4
• Both: add a denominator of 2 for all

Step 2:

• Make a root of all denominators and simplify
• (1,0) coordinate = 0◦ = 2π

Question 7

Remembering how to draw unit circle w/16 special angles

Quadrant 2: (x, y), (cosine, sine) coordinates

Answer 7

• Same values of Quadrant 1
• EXCEPT x value is negative

Question 8

Remembering how to draw unit circle w/16 special angles

Quadrant 4: (x, y), (cosine, sine) coordinates

Answer 8

• Same values of Quadrant 3
• EXCEPT y value is negative

Question 9

Remembering how to draw unit circle w/16 special angles

Quadrant 3: (x, y), (cosine, sine) coordinates

Answer 9

• Same values of Quadrant 1, BACKWARDS
• x & y value are negative

Question 10

All Students Take Calculus

Answer 10

Question 11

how to draw a right triangle in the unit circle

Answer 11

• put the acute angle at the origin (0,0)
• put the right angle on the x-axis

Question 12

obtuse angle

Answer 12

Obtuse angles can be from 90 degrees to 180 degrees.

Question 13

acute angle

Answer 13

• An acute angle (“acute” meaning “small”) is an angle smaller than a right angle.
• The range of an acute angle is between 0 and 90 degrees

Question 14

where are the cosine, sine and tangent of an angle on a unit circle?

Answer 14

Question 15

the terminal side of an angle in the unit circle shows the x-coordinate as the angle’s _____ and the y-coordinate as the angle’s _____. To remember this use the mnemonic:

Answer 15

• cosine
• sine
• x & y are in alphabetical order as are cosine and sine

Question 16

formula to convert degrees to radians and radians to degrees

Answer 16

Question 17

if 180° = π radians then

1. 90 equals _____ of π, or _____ radians
2. 60 equals _____ of π, or _____ radians
3. 45 equals ______ of π, or _____ radians
4. 30 equals ______ of π, or _____ radians

Answer 17

1. half, π/2
2. third, π/3
3. fourth, π/4
4. sixth, π/6

Question 18

360° equals _____ radians, so the unit circle’s circumference is _____. Half a circumference has a length of _____, so 180 equals _____ radians.

Answer 18

• 2π
• 2π
• π
• π

Question 19

If a circle has a radius of 1, it’s circumference equals ______. if an angle is 30°, it’s _____ of the circle circumference.

Answer 19

• 2π
• 30/360 = 1/12

Question 20

formula for circumference

Answer 20

C = 2πr

Question 21

radian

Answer 21

• radian measure of an angle is the length of the arc along the circumference of the unit circle cut off by the angle
• preferred over degrees

Question 22

To measure an angle in the unit circle, start at the positive _____ axis and go _____ to the ______ side of the angle. If you go _____ instead, you get an angle with a negative measure.

Answer 22

• x
• counterclockwise
• terminal
• clockwise

Question 23

Unit circle

Answer 23

• used to find values for any size angle
• has a radius of one unit
• set in an x-7 coordinate
• has center at the origin

Question 24

30°, 60°, 90° triangle

Answer 24

Question 25

45°, 45°, 90° triangle

solve for length of legs, given only the hypotenuse

Answer 25

Question 26

45°, 45°, 90° triangle

Answer 26

Question 27

Pythagorean Theorem

Answer 27

used to find the length of the side of a right triangle’s leg

Question 28

trig functions of right triangles

Answer 28

Question 29

_____ is the reciprocal of sine. _____ is the reciprocal of cosine. _____ is the reciprocal of tangent.

Answer 29

• cosecant (csc)
• secant (sec)
• cotangent (cot)

Question 30

SoCahToah

Answer 30

• only works with right triangles
• can only handle acute angles: angles < 90°

Question 31

The longest side of a right triangle is the ______ side, the _____. The side touching the selected angle is called the ______ side. The side across from the angle is called the _____ side.

Answer 31

• diagonal
• hypotenuse
• adjacent
• opposite

Question 32

trig functions & unit circle values

• sin
• cos
• tan
• cot
• sec
• csc

Answer 32

where r = radius of unit circle = 1

• sin = x
• cos = y
• tan = y / x
• cot = x / y
• sec = r / x
• csc = r / y