PRO Trig

Question 1

What function can be placed over one to get csc?

Answer 1

Sin

Question 2

What function can be placed over one to get sec?

Answer 2

Cos

Question 3

What function can be placed over one to get cot?

What functions can be placed over each other to get cot?

Answer 3

Tan, Cos/Sin

Question 4

What function can be placed over one to get sin?

Answer 4

Csc

Question 5

What function can be placed over one to get cos?

Answer 5

Sec

Question 6

What function can be placed over one to get tan?

What functions can be placed over each other to get tan?

Answer 6

Cot, Sin/Cos

Question 7

What is the first “Pythagorean” identity?

Answer 7

Sin^2 + Cos^2 = 1

Question 8

How do you get the second and third “Pythagorean” identities?

Answer 8

Divide by Sin^2 and Cos^2

Question 9

What are sin, cos, and tan in terms of x and y? (On the unit circle)

Answer 9

Sin=Y, Cos=x, and Tan=y/x

Question 10

What is sin(-t)?

Answer 10

-Sin(t)

Question 11

What is cos(-t)?

Answer 11

Cos(t)

Question 12

What is tan(-t)?

Answer 12

-Tan(t)

Question 13

What is sin(a+b)?

Answer 13

Sin(a)Cos(b) + Cos(a)Sin(b)

Question 14

What is sin(a-b)?

Answer 14

Sin(a)Cos(b) - Cos(a)Sin(b)

Question 15

What is cos(a+b)?

Answer 15

Cos(a)Cos(b) - Sin(a)*Sin(b)

Question 16

What is cos(a-b)?

Answer 16

Cos(a)Cos(b) + Sin(a)*Sin(b)

Question 17

What is tan(a+b)?

Answer 17

(Tan(a)+Tan(b))/(1-Tan(a)*Tan(b))

Question 18

What is tan(a-b)?

Answer 18

(Tan(a)-Tan(b))/(1+Tan(a)*Tan(b))

Question 19

What is Sin(2a)?

Answer 19

2Sin(a)Cos(a)

Question 20

What is Cos(2a)?

Answer 20

Cos^2(a)-Sin^2(a), which you can use the first P identity to get 1-2Sin^2(a) or 2Cos(a)^2-1

Question 21

What is Tan(2a)?

Answer 21

(2*Tan(a))/(1-Tan(a)^2)

Question 22

What is Sin(a/2)?

Answer 22

+/- The square root of (1-Cos(a))/2

Question 23

What is Cos(a/2)?

Answer 23

+/- The square root of (1+Cos(a))/2

Question 24

What is Tan(a/2)?

Answer 24

+/- The square root of (1-Cos(a))/(1+Cos(a)) which is equal to (1-Cos(a))/Sin(a) or Sin(a)/(1+Cos(a))

Question 25

What is Sin(x) + Sin(y)? (Might not need to know)

Answer 25

2*Sin(x+y over 2)*Cos(x-y over 2)

Question 26

What is Sin(x) - Sin(y)? (Might not need to know)

Answer 26

2*Sin(x-y over 2)*Cos(x+y over 2)

Question 27

What is Cos(x) + Cos(y)? (Might not need to know)

Answer 27

2*Cos(x-y over 2)*Cos(x+y over 2)

Question 28

What is Cos(x) - Cos(y)? (Might not need to know)

Answer 28

-2*Sin(x-y over 2)*Sin(x+y over 2)

Question 29

What is Sin(x)*Cos(y)? (Might not need to know)

Answer 29

.5[Sin(x+y)+Sin(x-y)]

Question 30

What is Cos(x)*Sin(y)? (Might not need to know)

Answer 30

.5[Sin(x+y)-Sin(x-y)]

Question 31

What is Cos(x)*Cos(y)? (Might not need to know)

Answer 31

.5[Cos(x+y)+Cos(x-y)]

Question 32

What is Sin(x)*Sin(y)? (Might not need to know)

Answer 32

.5[Cos(x-y)-Cos(x+y)]

Question 33

What is the period of the normal sin and cos graphs?

Answer 33

2pie

Question 34

What is the period of tan and cot?

Answer 34

Pie

Question 35

What is the period of sec and csc?

Answer 35

2pie

Question 36

What is the amplitude of any trig function?

Answer 36

Tan, Cot, Sec, and Csc have no amplitude, the amplitude of sin and cos is the (absolute value of the) number in front of the function

Question 37

What is the formula for the period of a trig function?

Answer 37

regular period/the absolute value of the number inside the parenthesis of the function

Question 38

What is the phase shift of Trig(x+pie)?

Answer 38

Pie to the left

Question 39

What is the phase shift of Sin(Bx-C)?

Answer 39

C/B to the right

Question 40

What is the sin rule?

Answer 40

Sin(A)/a = Sin(B)/b = Sin(C)/c

Question 41

What is the cos rule?

Answer 41

The Opposite Side^2=Side^2 + Side^2 - 2*side*side*Cos(angle)

Question 42

How do you find the area of a triangle using the sine rule?

Answer 42

1/2 * a * b * Sin(C)

Question 43

What is the point associated with 0*?

Answer 43

(1,0)

Question 44

What is the point associated with 30* or pie/6?

Answer 44

(Square root of 3 over 2, 1/2)

Question 45

What is the point associated with 45* or pie/4?

Answer 45

(Square root of 2 over 2, "")

Question 46

What is the point associated with 60* or pie/3?

Answer 46

(1/2, Square root of 3 over 2)

Question 47

What is the phrase used with trig functions and right triangles?

Answer 47

SOH-CAH-TOA

Question 48

How do you convert between radians and degrees?

Answer 48

pie/180*

Question 49

What are the values of the sides of a 45* right triangle?

Answer 49

1,1,Square root of 2

Question 50

What are the values of the sides of a 30* right triangle?

Answer 50

1,2,Square root of 3

Question 51

What is Sin(90*-t)?

Answer 51

Cos(t)

Question 52

What is Tan(90*-t)?

Answer 52

Cot(t)

Question 53

What is Sec(90*-t)?

Answer 53

Csc(t)

Question 54

What is Cos(90*-t)?

Answer 54

Sin(t)

Question 55

What is Cot(90*-t)?

Answer 55

Tan(t)

Question 56

What is Csc(90*-t)?

Answer 56

Sec(t)

Question 57

What is Tan(30*)?

Answer 57

Square root of three over 3

Question 58

What is Tan(45*)?

Answer 58

1

Question 59

What is Tan(60*)?

Answer 59

Square root of three

Question 60

What Quadrants does Sin-1 need to be restricted to?

Answer 60

1 and 4

Question 61

What Quadrants does Cos-1 need to be restricted to?

Answer 61

1 and 2

Question 62

What Quadrants does Tan-1 need to be restricted to?

Answer 62

1 and 4

Question 63

What is the way to find out the area of a triangle given each side?

Answer 63

The square root of s*(s-a)*(s-b)*(s-c) | s=(a+b+c)/2