Trigonometric Exact Values and Identities

Question 1

What is the exact value of sin(0°)?

Answer 1

0

Question 2

What is the exact value of cos(0°)?

Answer 2

1

Question 3

What is the exact value of tan(45°)?

Answer 3

1

Question 4

True or False: sin(90°) equals 1.

Answer 4

True

Question 5

What is the exact value of sin(30°)?

Answer 5

1/2

Question 6

What is the exact value of cos(30°)?

Answer 6

√3/2

Question 7

What is the exact value of tan(30°)?

Answer 7

1/√3 or √3/3

Question 8

What is the exact value of sin(45°)?

Answer 8

√2/2 or 1/√2

Question 9

What is the exact value of cos(45°)?

Answer 9

√2/2 or 1/√2

Question 10

What is the exact value of sin(60°)?

Answer 10

√3/2

Question 11

What is the exact value of cos(60°)?

Answer 11

1/2

Question 12

What is the exact value of tan(60°)?

Answer 12

√3

Question 13

Fill in the blank: sin(180°) equals ____.

Answer 13

0

Question 14

What is the exact value of sin(90°)?

Answer 14

1

Question 15

What is the exact value of cos(90°)?

Answer 15

0

Question 16

What is the exact value of tan(90°)?

Answer 16

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Question 17

True or False: cos(180°) equals -1.

Answer 17

True

Question 18

What is the exact value of sin(270°)?

Answer 18

-1

Question 19

What is the exact value of cos(270°)?

Answer 19

0

Question 20

What is the exact value of tan(270°)?

Answer 20

undefined

Question 21

What is the exact value of sin(360°)?

Answer 21

0

Question 22

What is the exact value of cos(360°)?

Answer 22

1

Question 23

What is the exact value of tan(360°)?

Answer 23

0

Question 24

Fill in the blank: tan(0°) equals ____.

Answer 24

0

Question 25

What is the relationship between sin²(θ) and cos²(θ)?

Answer 25

sin²(θ) + cos²(θ) = 1

Question 26

What is the exact value of cos(120°)?

Answer 26

-1/2

Question 27

What is the exact value of sin(120°)?

Answer 27

√3/2

Question 28

What is the exact value of tan(120°)?

Answer 28

-√3

Question 29

What is the exact value of cos(135°)?

Answer 29

-√2/2 or -1/√2

Question 30

What is the Pythagorean identity for sine and cosine?

Answer 30

sin²(θ) + cos²(θ) = 1

Question 31

What is the addition formula for sin(a + b)?

Answer 31

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Question 32

True or False: cos(θ) = sin(90° - θ)

Answer 32

True

Question 33

Fill in the blank: The double angle formula for sin(2θ) is _____ .

Answer 33

sin(2θ) = 2sin(θ)cos(θ)

Question 34

What is the addition formula for cos(a + b)?

Answer 34

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Question 35

What is the double angle formula for cos(2θ)?

Answer 35

cos(2θ) = cos²(θ) - sin²(θ)

Question 36

What are the values of sin(0°) and cos(0°)?

Answer 36

sin(0°) = 0, cos(0°) = 1

Question 37

What is the formula for tan(a + b)?

Answer 37

tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

Question 38

True or False: sin(θ) = tan(θ)cos(θ)

Answer 38

True

Question 39

Fill in the blank: The identity tan(θ) can be expressed as _____ .

Answer 39

tan(θ) = sin(θ) / cos(θ)

Question 40

What is the formula for sin(a - b)?

Answer 40

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Question 41

What is the formula for cos(a - b)?

Answer 41

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Question 42

What is the complementary identity for sine?

Answer 42

sin(θ) = cos(90° - θ)

Question 43

True or False: The sum of the angles in a triangle is always 180°.

Answer 43

True

Question 44

What is the double angle formula for tan(2θ)?

Answer 44

tan(2θ) = 2tan(θ) / (1 - tan²(θ))

Question 45

What is the addition formula for tan(a + b) in terms of sine and cosine?

Answer 45

tan(a + b) = sin(a + b) / cos(a + b)

Question 46

Fill in the blank: The identity for the tangent function can also be expressed as _____ .

Answer 46

tan(θ) = sin(θ) / cos(θ)

Question 47

What is the relationship between sine and cosine for complementary angles?

Answer 47

sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ)