Trig

Question 1

the x-coordinate of the point t
on the number circle.

Answer 1

cos t

Question 2

the y-coordinate of the point t
on the number circle.

Answer 2

sin t

Question 3

Period of Cosine

Answer 3

2pi

Question 4

Period of Sine

Answer 4

2pi

Question 5

cis(t) =

Answer 5

cos(t) + isin(t)

Question 6

Is Cosine an even or odd function

Answer 6

Even

Question 7

Formula for coterminal angles of cos

Answer 7

cos(t + 2kpi)

Question 8

Is Sine an even or odd function

Answer 8

Odd

Question 9

Formula for coterminal angles of sin

Answer 9

Sin(t + 2kpi)

Question 10

Equation of the Unit Circle

Answer 10

x^2 + y^2 = 1

Question 11

projection of t through the origin to the s-axis.

Also the slope of the line through the origin and t

Answer 11

tan t

Question 12

projection of t through the origin to the r-axis.

Also the reciprocal slope of the line through the origin and t

Answer 12

cot t

Question 13

What is the period of tan

Answer 13

pi

Question 14

is tangent an even or odd function

Answer 14

odd

Question 15

cos co-function identity

Answer 15

sin(pi/2 - t)

Question 16

sin co-function identity

Answer 16

cos(pi/2 - t)

Question 17

tan co-function identity

Answer 17

cot(pi/2 - t)

Question 18

cot co-function identity

Answer 18

tan(pi/2 - t)

Question 19

Is secant an even or odd function

Answer 19

even

Question 20

Is Cosecant an even or odd function

Answer 20

odd

Question 21

what are the periods of sec and csc

Answer 21

2kpi

Question 22

reciprocal identity of csc(t)

Answer 22

1/sin(t)

Question 23

reciprocal identity of sec(t)

Answer 23

1/cos(t)

Question 24

reciprocal identity of cot(t)

Answer 24

1/tan(t)

Question 25

reciprocal identity of sin(t)

Answer 25

1/csc(t)

Question 26

reciprocal identity of cos(t)

Answer 26

1/sec(t)

Question 27

reciprocal identity of tan(t)

Answer 27

1/cot(t)

Question 28

quotient identity of tan(t)

Answer 28

sin(t)/cos(t)

Question 29

tangent is positive in which quadrants

Answer 29

1 and 3

Question 30

sine is positive in which quadrants

Answer 30

1 and 2

Question 31

cosine is positive in which quadrants

Answer 31

1 and 4

Question 32

amplitude for sine and cosine

Answer 32

distance between top and bottom of wave divided by 2

Question 33

phase shift for sine and cosine

Answer 33

location of the peak closest to the x axis

Question 34

baseline

Answer 34

the mid-point of the wave

Question 35

formula for the period of sine and cosine

Answer 35

2pi / omega (ω)

Question 36

formula for phase shift

Answer 36

- phi (φ) / omega (ω)

Question 37

What is the amplitude of the following: 3 sin (4t + pi/3) + 5

Answer 37

3

Question 38

What is the baseline of the following: 3 sin (4t + pi/3) + 5

Answer 38

5

Question 39

What is the phase of the following: 3 sin (4t + pi/3) + 5

Answer 39

pi/3

Question 40

What is the period of the following: 3 sin (4t + pi/3) + 5

Answer 40

2pi/4

Question 41

What is the phase shift of the following: 3 sin (4t + pi/3) + 5

Answer 41

- (pi/3) / 4

Question 42

What is the formula for the period of Tangent

Answer 42

pi / omega (ω)

Question 43

How do you find the amplitude of Tangent

Answer 43

period / 4

Question 44

How do you find the asymptote of Tangent

Answer 44

period / 2

Question 45

Transformations formula for cosine

Answer 45

f(t) = a cos (ωt + φ) + b

Question 46

Where is the phase shift of Cotangent

Answer 46

The Asymptote

Question 47

How do you find the amplitude of Cotangent

Answer 47

period / 4

Question 48

Where is the period of cotangent

Answer 48

From asymptote to asymptote

Question 49

formula to find Tangent

Answer 49

y/x or sin/cos

Question 50

formula to find Cotangent

Answer 50

x/y or cos/sin

Question 51

cosine addition formula

Answer 51

cos(s + t) = cos(s) * cos(t) - sin(s) * sin(t)

Question 52

sine addition formula

Answer 52

sin(s + t) = cos(s) * sin(t) + sin(s) * cos(t)

Question 53

tangent addition formula (without simplification)

Answer 53

tan(s + t) = sin(s + t) / cos(s + t)

Question 54

tangent addition formula (simplified)

Answer 54

tan(t) + tan(s) / 1 - tan(t) * tan(s)

Question 55

cosine subtraction formula

Answer 55

cos(s - t) = cos(s) * cos(t) + sin(s) * sin(t)

Question 56

sine subtraction formula

Answer 56

sin(s - t) = sin(s) * cos(t) − cos(s) * sin(t)

Question 57

cosine double-angle formula

Answer 57

cos(2t) = cos^2(t) - sin^2(t)

Question 58

sine double-angle formula

Answer 58

sin(2t) = 2cos(t)sin(t)

Question 59

tangent subtraction formula

Answer 59

tan(α−β)= tan(α)−tan(β) / 1+tan(α)tan(β)

Question 60

tangent double-angle formula

Answer 60

tan(2t) = 2tan(t) / 1 - tan^2(t)