Trigonometry for SAT, ACT and AP Precalculus flashcards

Question 1

For an angle θ, what is tan(θ) in terms of sin(θ) and cos(θ)?

Accepted Answer

tan(θ) = sin(θ)/cos(θ)

Question 2

For an angle θ, what is csc(θ) in terms of sin(θ)?

Accepted Answer

csc(θ) = 1/sin(θ)

Question 3

For an angle θ, what is sec(θ) in terms of cos(θ)?

Accepted Answer

sec(θ) = 1/cos(θ)

Question 4

For an angle θ, what is cot(θ) in terms of sin(θ) and cos(θ)?

Accepted Answer

cot(θ) = cos(θ)/sin(θ)

Question 5

For an angle θ, what is cot(θ) in terms of tan(θ)?

Accepted Answer

cot(θ) = 1/tan(θ)

Question 6

In a right triangle, what is cos of an acute angle in terms of the sides?

Accepted Answer

The length of the side next to the angle (other than the hypotenuse) divided by the length of the hypotenuse: cos = adjacent/hypotenuse.

Question 7

What is the hypotenuse of a right triangle?

Accepted Answer

The side opposite the right angle; it is the longest of the three sides.

Question 8

In a right triangle, the two acute angles together measure how many radians?

Accepted Answer

π/2 radians (90°)

Question 9

In a right triangle with legs a and b and hypotenuse h, what does the Pythagorean theorem state?

Accepted Answer

h² = a² + b²

Question 10

A full circle measures 360 degrees. How many radians is that?

Accepted Answer

2π radians

Question 11

How many degrees is one radian equal to, as an exact expression?

Accepted Answer

1 radian = 180/π degrees

Question 12

How many radians is one degree equal to, as an exact expression?

Accepted Answer

1 degree = π/180 radians

Question 13

By what factor do you multiply an angle in degrees to get radians?

Accepted Answer

π/180

Question 14

By what factor do you multiply an angle in radians to get degrees?

Accepted Answer

180/π

Question 15

What is sin(0), with the angle in radians?

Accepted Answer

0

Question 16

What is cos(0), with the angle in radians?

Accepted Answer

1

Question 17

What is tan(0), with the angle in radians?

Accepted Answer

0

Question 18

What is sin(π/6), with the angle in radians?

Accepted Answer

1/2

Question 19

What is cos(π/6), with the angle in radians?

Accepted Answer

(√3)/2

Question 20

What is tan(π/6), with the angle in radians?

Accepted Answer

(√3)/3

Question 21

What is sin(π/4), with the angle in radians?

Accepted Answer

(√2)/2

Question 22

What is cos(π/4), with the angle in radians?

Accepted Answer

(√2)/2

Question 23

What is tan(π/4), with the angle in radians?

Accepted Answer

1

Question 24

What is sin(π/3), with the angle in radians?

Accepted Answer

(√3)/2

Question 25

What is cos(π/3), with the angle in radians?

Accepted Answer

1/2

Question 26

What is tan(π/3), with the angle in radians?

Accepted Answer

√3

Question 27

What is sin(π/2), with the angle in radians?

Accepted Answer

1

Question 28

What is cos(π/2), with the angle in radians?

Accepted Answer

0

Question 29

What is csc(π/6), with the angle in radians?

Accepted Answer

2

Question 30

What is sec(π/3), with the angle in radians?

Accepted Answer

2

Question 31

What is cot(π/4), with the angle in radians?

Accepted Answer

1

Question 32

For an angle θ, what is sin²(θ) + cos²(θ)?

Accepted Answer

1

Question 33

For an angle θ, what does sec²(θ) equal in terms of tan(θ)?

Accepted Answer

sec²(θ) = 1 + tan²(θ)

Question 34

For an angle θ, what does csc²(θ) equal in terms of cot(θ)?

Accepted Answer

csc²(θ) = 1 + cot²(θ)

Question 35

For angles u and v, what is sin(u + v)?

Accepted Answer

sin(u)cos(v) + cos(u)sin(v)

Question 36

For angles u and v, what is sin(u − v)?

Accepted Answer

sin(u)cos(v) − cos(u)sin(v)

Question 37

For angles u and v, what is cos(u + v)?

Accepted Answer

cos(u)cos(v) − sin(u)sin(v)

Question 38

For angles u and v, what is cos(u − v)?

Accepted Answer

cos(u)cos(v) + sin(u)sin(v)

Question 39

For angles u and v, what is tan(u + v) in terms of tan(u) and tan(v)?

Accepted Answer

(tan(u) + tan(v))/(1 − tan(u)tan(v))

Question 40

For an angle θ, what is sin(2θ) in terms of sin(θ) and cos(θ)?

Accepted Answer

sin(2θ) = 2 sin(θ) cos(θ)

Question 41

For an angle θ, what is cos(2θ) in terms of cos(θ) and sin(θ), as a difference of squares?

Accepted Answer

cos(2θ) = cos²(θ) − sin²(θ)

Question 42

For an angle θ, what is cos(2θ) in terms of cos(θ) only?

Accepted Answer

cos(2θ) = 2cos²(θ) − 1

Question 43

For an angle θ, what is cos(2θ) in terms of sin(θ) only?

Accepted Answer

cos(2θ) = 1 − 2sin²(θ)

Question 44

For an angle θ, what is tan(2θ) in terms of tan(θ)?

Accepted Answer

tan(2θ) = 2tan(θ)/(1 − tan²(θ))

Question 45

For an angle θ, what is tan(−θ)?

Accepted Answer

tan(−θ) = −tan(θ)

Question 46

For an angle θ in radians, what is sin(π/2 − θ)?

Accepted Answer

cos(θ)

Question 47

For an angle θ in radians, what is cos(π/2 − θ)?

Accepted Answer

sin(θ)

Question 48

For an angle θ in radians, what is tan(π/2 − θ)?

Accepted Answer

cot(θ)

Question 49

For any integer k and angle θ in radians, what is sin(θ + 2kπ)?

Accepted Answer

sin(θ); adding any whole number of full turns (2π) leaves sine unchanged

Question 50

For any integer k and angle θ in radians, what is cos(θ + 2kπ)?

Accepted Answer

cos(θ); adding any whole number of full turns (2π) leaves cosine unchanged

Question 51

For any integer k and angle θ in radians, what is tan(θ + kπ)?

Accepted Answer

tan(θ); adding any whole multiple of π leaves tangent unchanged

Question 52

In which quadrants is sin(θ) positive (quadrants I to IV)?

Accepted Answer

Quadrants I and II (negative in III and IV)

Question 53

In which quadrants is cos(θ) positive (quadrants I to IV)?

Accepted Answer

Quadrants I and IV (negative in II and III)

Question 54

In which quadrants is tan(θ) positive (quadrants I to IV)?

Accepted Answer

Quadrants I and III (negative in II and IV)

Trigonometry for SAT, ACT and AP Precalculus flashcards

The cards

How this deck was checked

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Trigonometry for SAT, ACT and AP Precalculus flashcards

The cards

How this deck was checked

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