Trigonometric Formulas & Graphs

Question 1

sin x 的图像

Answer 1

Question 2

cos x 的图像

Answer 2

Question 3

tan x 的图像

Answer 3

Question 4

arcsin x 的主值区间与图像

Answer 4

[-0.5π, 0.5π]

Question 5

arccos x 的主值区间与图像

Answer 5

[0, π]

Question 6

arctan x 的主值区间与图像

Answer 6

(-0.5π, 0.5π)

Question 7

cot x 的图像

Answer 7

Question 8

arccot x 的主值区间与图像

Answer 8

(0, π)

Question 9

sec x 的图像

sec x = 1/__?

Answer 9

cos x

Question 10

csc x 的图像

csc x = 1/__?

Answer 10

sin x

Question 11

设 u=tan x/2, 用 u 表示 sin x.

Answer 11

sinx = 2u/(1+u²)

sin x = 2·sin x/2·cos x/2 = 2u/sec²(x/2) = 2u/(1+u²)

Question 12

设 u = tan x/2, 用 u 表示 cos x.

Answer 12

cos x = (1-u²)/(1+u²).

cos x = cos²x/2-sin²x/2 = [1-u²]/sec²(x/2) = (1-u²)/(1+u²).

Question 13

正弦定理

Answer 13

a/sinA = b/sinB = c/sinC = 2R

其中 R 表示三角形的外接圆半径

Question 14

余弦定理

Answer 14

b²=a²+c²-2·a·c·cosB

Question 15

正切定理

Answer 15

Question 16

sin(A±B) = ?

cos(A±B) = ?

Answer 16

sin(A±B) = sinAcosB ± cosAsinB

cos(A±B) = cosAcosB ∓ sinAsinB

Question 17

tan(A±B) = ?

Answer 17

tan(A±B) = (tanA ± tanB) / (1 ∓ tanA·tanB)

Question 18

cot(A±B) = ?

Answer 18

cot(A±B) = (cotA·cotB ∓ 1) / (cotB ± cotA)

Question 19

sin 2x = ?

Answer 19

sin 2x = 2·sin x· cos x

Question 20

cos 2x = ①? = ②? = ③?

Answer 20

① cos²x-sin²x
② 2cos²x-1

③ 1- 2sin²x

Question 21

tan 2α = ?

Answer 21

Question 22

sin 3x = ?

Answer 22

sin 3x = 3·sin x - 4·(sin x)³

Question 23

cos 3x = ?

Answer 23

cos 3x = 4·(cos x)³ - 3·cos x

Question 24

tan 3x = ?

Answer 24

tan 3x = tan x· tan(π/3+x)· tan(π/3-x)

Question 25

sin A/2

Answer 25

Question 26

cos A/2

Answer 26

Question 27

tan A/2

tan θ/2

Answer 27

Question 28

积化和差 sin

Answer 28

Question 29

积化和差 cos

Answer 29

Question 30

积化和差 tan

Answer 30

Question 31

sin θ ± sin φ 化为积式.

Answer 31

Question 32

cos θ + cos φ 化为积式.

Answer 32

Question 33

cos θ - cos φ 化为积式.

Answer 33

Question 34

用 tan a/2 表示 tan a

Answer 34

2u/(1-u²)

Question 35

sin²α 降幂公式

Answer 35

Question 36

cos²α 降幂公式

Answer 36

Question 37

(2n)!! = ?

Answer 37

Question 38

a³-b³ = ?

Answer 38

Question 39

a³+b³ = ?

Answer 39

Question 40

将 aⁿ-bⁿ 分解为 (a-b) 的因式

Answer 40

Question 41

将 aⁿ-bⁿ 分解为 (a+b) 的因式

Answer 41

Question 42

将 aⁿ+bⁿ 分解为 (a+b) 的因式

Answer 42

Question 43

1+2+3+4+…+n = ?

Answer 43

n(n+1)/2

Question 44

1+3+5+…+(2n-1) = ?

Answer 44

n²

Question 45

2+4+6+…+(2n) = ?

Answer 45

n(n+1)

Question 46

1²+2²+3²+…+n² = ?

Answer 46

n(n+1)(2n+1)/6

Question 47

1³+2³+3³+…n³ = ?

Answer 47

n²(n+1)²/4

Question 48

1×2+2×3+3×4+4×5+…+n(n+1) = ?

Answer 48

n(n+1)(n+2)/3

Question 49

韦达定理

Answer 49

x₁+x₂ = -b/a

x₁×x₂ = c/a

Question 50

1 + sin a = ( ? )²

Answer 50

Question 51

1 - sin a = ( ? )²

Answer 51

Question 52

sinh a = ?

Answer 52

Question 53

cosh a = ?

Answer 53