sin x |
sin-1 x |
sec x |
csc x |
tan x |
tan-1 x |
cos x |
cos-1 x |
sec-1 x |
csc-1
x |
cot x |
cot-1 x |
sinh x |
cosh x |
tanh x |
sinh-1 x |
cosh-1 x |
tanh-1 x |
グラフの形状 |
グラフの勾配 |
x=2nπの時勾配=1 x=(2n-1)πの時勾配=-1 x=nπ+π/2の時勾配=0 |
x[rad] |
x[°] |
sin(x) |
cos(x) |
tan(x) |
-π/2 -π |
-90 -180 |
-1 0 |
0 -1 |
±∞ 0 |
0 π/60 π/30 π/20 π/18 π/15 π/12 π/10 π/9 7π/60 π/8 2π/15 5π/36 3π/20 π/6 11π/60 π/5 13π/60 2π/9 7π/30 |
0 3 6 9 10 12 15 18 20 21 22.5 24 25 27 30 33 36 39 40 42 |
0 (-2√(15+3√5)+2√(5+√5)+√30+√10-√6-√2)/16 (√(30-6√5)-√5-1)/8 (-2√(5-√5)+√10+√2)/8 - (√(10+2√5)-√15+√3)/8 (√6-√2)/4 (√5-1)/4 - (2√(15-3√5)+2√(5-√5)-√30+√10-√6+√2)/16 {√(2-√2)}/2 (-√(10-2√5)+√15+√3)/8 - (2√(5+√5)-√10+√2)/8 1/2 (2√(15+3√5)-2√(5+√5)+√30+√10-√6-√2)/16 √(10-2√5)/4 (-2√(15-3√5)+2√(5-√5)+√30+√10+√6+√2)/16 - (√(30+6√5)-√5+1)/8 |
1 (2√(15+3√5)+2√(5+√5)+√30-√10-√6+√2)/16 (√(10-2√5)+√15+√3)/8 (2√(5-√5)+√10+√2)/8 - (√(30+6√5)+√5-1)/8 (√6+√2)/4 √(10+2√5)/4 - (2√(15-3√5)-2√(5-√5)+√30+√10+√6+√2)/16 {√(2+√2)}/2 (√(30-6√5)+√5+1)/8 - (2√(5+√5)+√10-√2)/8 √3/2 (2√(15+3√5)+2√(5+√5)-√30+√10+√6-√2)/16 (√5+1)/4 (2√(15-3√5)+2√(5-√5)+√30-√10+√6-√2)/16 - (√(10+2√5)+√15-√3)/8 |
0 - - - - - 2-√3 (5-√5)(√(10-2√5)/20 - - √2-1 - - - 1/√3 - - - - - |
π/4 | 45 | 1/√2 | 1/√2 | 1 |
4π/15 5π/18 17π/60 3π/10 19π/60 π/3 7π/20 11π/30 3π/8 23π/60 7π/18 2π/5 5π/12 13π/30 4π/9 9π/20 7π/15 29π/60 π/2- |
48 50 51 54 57 60 63 66 67.5 69 70 72 75 78 80 81 84 87 90- |
(√(10+2√5)+√15-√3)/8 - (2√(15-3√5)+2√(5-√5)+√30-√10+√6-√2)/16 (√5+1)/4 (2√(15+3√5)+2√(5+√5)-√30+√10+√6-√2)/16 √3/2 (2√(5+√5)+√10-√2)/8 (√(30-6√5)+√5+1)/8 {√(2+√2)}/2 (2√(15-3√5)-2√(5-√5)+√30+√10+√6+√2)/16 - √(10+2√5)/4 (√6+√2)/4 (√(30+6√5)+√5-1)/8 - (2√(5-√5)+√10+√2)/8 (√(10-2√5)+√15+√3)/8 (2√(15+3√5)+2√(5+√5)+√30-√10-√6+√2)/16 1 |
(√(30+6√5)-√5+1)/8 - (-2√(15-3√5)+2√(5-√5)+√30+√10+√6+√2)/16 √(10-2√5)/4 (2√(15+3√5)-2√(5+√5)+√30+√10-√6-√2)/16 1/2 (2√(5+√5)-√10+√2)/8 (-√(10-2√5)+√15+√3)/8 {√(2-√2)}/2 (2√(15-3√5)+2√(5-√5)-√30+√10-√6+√2)/16 - (√5-1)/4 (√6-√2)/4 (√(10+2√5)-√15+√3)/8 - (-2√(5-√5)+√10+√2)/8 (√(30-6√5)-√5-1)/8 (-2√(15+3√5)+2√(5+√5)+√30+√10-√6-√2)/16 0 |
- - - - - √3 - - √2+1 - - (√5+1)√(10+2√5) /4 2+√3 - - - - - ∞ |
π/2 | 90 | 1 | 0 | 未定義 |
π/2+ 7π/12 3π/5 2π/3 3π/4 5π/6 9π/10 11π/12 π |
90+ 105 108 120 135 150 168 165 180 |
1 (√6+√2)/4 √(10+2√5)/4 √3/2 1/√2 1/2 (√5-1)/4 (√6-√2)/4 0 |
0 -(√6-√2)/4 -(√5-1)/4 -1/2 - 1/√2 - √3/2 -√(10+2√5)/4 -(√6+√2)/4 -1 |
-∞ -2-√3 -(√5+1)√(10+2√5) /4 -√3 -1 -1/√3 -(5-√5)(√(10-2√5)/20 -2+√3 0 |
積分範囲x=0〜a |
面積∫[0→a] sin(x)dx |
a=π/6 a=π/4 a=π/3 a=π/2 a=2π/3 a=3π/4 a=5π/6 a=π |
1-√3/2 1-1/√2 1/2 1 3/2 1+1/√2 1+√3/2 2 |
dsin(x)/dx |
cos(x) |
x=0 x=π/4 x=π/3 x=π/2 x=2π/3 x=π/4 x=π |
1 1/√2=0.7071067814 1/2=0.5 0 -1/2=-0.5 -1/√2=-0.7071067814 -1 |
グラフの概形 |
グラフの勾配 |
y=cos x |
x=nπの時勾
配=0 x=2nπ+(π/2)の時勾配=-1 x=2nπ-π/2の時勾配=1 y'=-sin x |
積分範囲x=0〜a |
面積∫[0→a] cos(x)dx |
a=π/6 a=π/4 a=π/3 a=π/2 a=2π/3 a=3π/4 a=5π/6 a=π |
1/2=0.5 1/√2=0.7071065 √3/2=0.866025 1 √3/2=0.866025 1/√2=0.7071065 1/2=0.5 0 |
dcos(x)/dx |
-sin(x) |
x=0 x=π/6 x=π/4 x=π/3 x=π/2 x=2π/3 x=3π/4 x=5π/6 x=π x=3π/2 x=2π |
0 -1/2=-0.5 -1/√2=-0.7071067814 -√3/2=-0.8660254 -1 -√3/2==-0.8660254 -1/√2=-0.7071067814 -1/2=0.5 0 1 0 |
x [rad] |
x [°] |
sin x |
cos x |
0 π/18 π/12 π/10 π/6 π/4 π/3 4π/10 5π/12 π/2 2π/3 3π/4 5π/6 9π/10 11π/12 π |
0 10 15 18 30 45 60 72 75 90 120 135 150 162 165 180 |
0 - (√6-√2)/4 (√5-1)/4 1/2=0.5 1/√2=0.7071 √3/2 - (√6+√2)/4 1 √3/2 1/√2=0.7071 1/2=0.5 (√5-1)/4 (√6-√2)/4 0 |
1 - (√6+√2)/4 - √3/2 1/√2=0.7071 1/2=0.5 (√5-1)/4 (√6-√2)/4 0 -1/2=-0.5 -1/√2=-0.7071 -√3/2 - -(√6+√2)/4 -1 |
x [rad] |
x [°] |
tan x |
-π/2 - 5π/12 - 2π/5 -π/3 -π/4 -π/6 - π/10 - π/12 - π/18 0 π/18 π/12 π/10 π/9 π/6 π/4 π/3 2π/5 5π/12 π/2 7π/12 3π/5 2π/3 3π/4 5π/6 9π/10 11π/12 17π/18 π |
-90 -75 -72 -60 -45 -30 -18 -15 -10 0 10 15 18 20 30 45 60 72 75 90 105 108 120 135 150 162 165 170 180 |
±∞ -2-√3 - -√3 -1 -1/√3 - -2+√3 - 0 - 2-√3 - - 1/ √3 1 √3 - 2+√3 ±∞ -2-√3 - -√3 -1 -1/√3 - -2+√3 - 0 |
A>0,B>0、A2+B2=1
のとき sin-1(A)=cos-1(B)=tan-1(A/B) =(π/2)-sin-1B =(π/2)-cos-1A =(π/2)-tan-1(B/A) |