Section 1

Question 1

True or False: tan(θ) = sin(θ) / cos(θ)

Answer 1

True

Question 2

What is the co-function identity for sin(θ)?

Answer 2

sin(θ) = cos(90° - θ)

Question 3

Which identity expresses tan(θ) in terms of sin and cos?

Answer 3

tan(θ) = sin(θ) / cos(θ)

Question 4

True or False: sec(θ) is the reciprocal of cos(θ).

Answer 4

True

Question 5

Fill in the blank: The identity for cot(θ) is ____.

Answer 5

1/tan(θ)

Question 6

What is the relationship between cosecant and sine?

Answer 6

csc(θ) = 1/sin(θ)

Question 7

True or False: cos(90° - θ) = sin(θ).

Answer 7

True

Question 8

Fill in the blank: The identity for sec(θ) is ____.

Answer 8

1/cos(θ)

Question 9

True or False: The tangent function is periodic with a period of π.

Answer 9

True

Question 10

Fill in the blank: The cotangent function is defined as ____.

Answer 10

1/tan(θ)

Question 11

What is the co-function identity for cos(θ)?

Answer 11

cos(θ) = sin(90° - θ)

Question 12

What is the formula for cos²(θ) in terms of sin²(θ)?

Answer 12

cos²(θ) = 1 - sin²(θ)

Question 13

True or False: The sine function is an odd function.

Answer 13

True

Question 14

What is the sine of an angle in a right triangle?

Answer 14

The ratio of the length of the opposite side to the length of the hypotenuse.

Question 15

What is the cosine of an angle in a right triangle?

Answer 15

The ratio of the length of the adjacent side to the length of the hypotenuse.

Question 16

What is the tangent of an angle in a right triangle?

Answer 16

The ratio of the length of the opposite side to the length of the adjacent side.

Question 17

True or False: The sine function is defined for all real numbers.

Answer 17

True.

Question 18

What is the relationship between the sine and cosine functions? - cofunction of sin

Answer 18

sin(θ) = cos(90° - θ)

Question 19

Which function can be defined as the ratio of sine to cosine?

Answer 19

Tangent

Question 20

What is the period of the sine and cosine functions?

Answer 20

2π radians or 360 degrees.

Question 21

What is the definition of the cotangent function?

Answer 21

The cotangent function is defined as the ratio of the adjacent side to the opposite side in a right triangle, or cot(x) = 1/tan(x).

Question 22

True or False: The cotangent function is the reciprocal of the tangent function.

Answer 22

True

Question 23

Fill in the blank: The cotangent of an angle x can be expressed as cot(x) = ____.

Answer 23

cos(x) / sin(x)

Question 24

What is the period of the cotangent function?

Answer 24

The period of the cotangent function is π.

Question 25

Multiple Choice: Which of the following is NOT a property of the cotangent function? A) It is undefined at integer multiples of π. B) It is an even function. C) It has a period of π. D) It can take any real number value.

Answer 25

B) It is an even function.

Question 26

What is the definition of the sine function in a right triangle?

Answer 26

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

Question 27

True or False: The sine of an angle is always between -1 and 1.

Answer 27

True

Question 28

Fill in the blank: The sine of 90 degrees is ____.

Answer 28

1

Question 29

What is the sine of 0 degrees?

Answer 29

0

Question 30

Which of the following is the correct formula for the sine of an angle θ in a unit circle? A) sin(θ) = y/r B) sin(θ) = x/r C) sin(θ) = r/y

Answer 30

A) sin(θ) = y/r

Question 31

What is the length of a circular arc intercepted by the central angle ?

Answer 31

S= r times theta

Question 32

What is the area of a sector formed by the central angle?

Answer 32

A= 1/2 r ^2 theta

Question 33

If point is in motion on a Circe:

Answer 33

W= theta/ t

Question 34

Linear speed of a point?

Answer 34

V=r w

Question 35

Cosecant equals?

Answer 35

Hypotenuse / opposite or 1/ sin theta

Question 36

Secant equals?

Answer 36

.hypotenuse/adjacent or 1/ cos theta

Question 37

Cotangent equals?

Answer 37

.adjacent / opposite or 1/ tan theta

Question 38

The quotient identity of cotangent is?,

Answer 38

- Cosine theta over sin theta

Question 39

What is the cofunction of tangent?

Answer 39

Cot( 90 degrees- theta )

Question 40

Cofunction of secant is?

Answer 40

Cosecant(90 degrees- theta)

Question 41

Cofunction of cot =?

Answer 41

Tan (90 degrees- theta)

Question 42

The reciprocal identity for tan is?

Answer 42

1/ cot theta

Question 43

Function of sin theta =?

Answer 43

Y/r

Question 44

Function of cos theta =?

Answer 44

X/r

Question 45

Function of tangent theta =?

Answer 45

Y/x when x isn't O

Question 46

Function of csc theta =?

Answer 46

R/y

Question 47

Function of sec =?

Answer 47

R/x

Question 48

Function of cot theta =?

Answer 48

X/y

Question 49

R=

Answer 49

Square root of x^2 + y^2

Question 50

Which functions are even?

Answer 50

Cos and sec

Question 51

Which functions are odd?

Answer 51

Sin csc tan and cot

Question 52

If p =(x,y) then what is sin of t?

Answer 52

Y

Question 53

If p =(x, y) then what is the cos of t?

Answer 53

X

Question 54

If p =(x,y) then what is tan of t?

Answer 54

Y/x

Question 55

Ifp =(x,y ) then what is csc of t?

Answer 55

1/y

Question 56

If p =(x,y) then what is sec of t?

Answer 56

1/ x

Question 57

If p =(x,y) then what is cot of t?

Answer 57

X/y

Question 58

What is the Pythagorean identity for sine and cosine?

Answer 58

sin²(θ) + cos²(θ) = 1

Question 59

True or False: tan²(θ) + 1 = sec²(θ).

Answer 59

True

Question 60

Fill in the blank: The identity sin²(θ) = 1 - _____.

Answer 60

cos²(θ)

Question 61

If sin(θ) = 3/5, what is cos(θ)?

Answer 61

4/5

Question 62

What is the Pythagorean identity for tangent and secant?

Answer 62

1 + tan²(θ) = sec²(θ)

Question 63

Which identity is derived from sin²(θ) + cos²(θ) = 1?

Answer 63

1 - sin²(θ) = cos²(θ)

Question 64

True or False: The identity 1 + cot²(θ) = csc²(θ) is a Pythagorean identity.

Answer 64

True