Save
Bicen Maths
Pure
Trigonometry
Save
Share
Learn
Content
Leaderboard
Learn
Created by
The Creator
Visit profile
Cards (10)
Radians to degrees conversion:
2
π
=
2\pi=
2
π
=
360
π
=
\pi=
π
=
180
π
2
\frac{\pi}{2}
2
π
=
90
π
3
=
\frac{\pi}{3}=
3
π
=
60
π
4
=
\frac{\pi}{4}=
4
π
=
45
π
6
=
\frac{\pi}{6}=
6
π
=
30
Small angle approximations
sin
θ
≈
\sin\theta\approx
sin
θ
≈
θ
\theta
θ
cos
θ
≈
\cos\theta\approx
cos
θ
≈
1
−
θ
2
2
1-\frac{\theta^2}{2}
1
−
2
θ
2
tan
θ
≈
\tan\theta\approx
tan
θ
≈
θ
\theta
θ
Exact sine trig values
sin
30
=
\sin30=
sin
30
=
1
2
\frac{1}{2}
2
1
sin
60
=
\sin60=
sin
60
=
3
2
\frac{\sqrt{3}}{2}
2
3
sin
45
=
\sin45=
sin
45
=
1
2
\frac{1}{\sqrt{2}}
2
1
Tangent defnition
tan
θ
=
\tan\theta=
tan
θ
=
sin
θ
cos
θ
\frac{\sin\theta}{\cos\theta}
c
o
s
θ
s
i
n
θ
Solving equations
sin
θ
=
\sin\theta=
sin
θ
=
sin
(
180
−
θ
)
\sin\left(180-\theta\right)
sin
(
180
−
θ
)
±
360
°
\pm360\degree
±
360°
cos
θ
=
\cos\theta=
cos
θ
=
cos
(
360
−
θ
)
\cos\left(360-\theta\right)
cos
(
360
−
θ
)
±
360
°
\pm360\degree
±
360°
tan
θ
=
\tan\theta=
tan
θ
=
tan
(
180
+
θ
)
\tan\left(180+\theta\ \right)
tan
(
180
+
θ
)
±
180
°
\pm180\degree
±
180°
Reciprocal trig functions
cosec
θ
=
\operatorname{cosec}\theta=
cosec
θ
=
1
sin
θ
\frac{1}{\sin\theta}
s
i
n
θ
1
sec
θ
=
\sec\theta=
sec
θ
=
1
cos
θ
\frac{1}{\cos\theta}
c
o
s
θ
1
cot
θ
=
\cot\theta=
cot
θ
=
1
tan
θ
\frac{1}{\tan\theta}
t
a
n
θ
1
Co-functions
sin
θ
=
\sin\theta=
sin
θ
=
cos
(
90
−
θ
)
\cos\left(90-\theta\right)
cos
(
90
−
θ
)
cos
θ
=
\cos\theta=
cos
θ
=
sin
(
90
−
θ
)
\sin\left(90-\theta\right)
sin
(
90
−
θ
)
Pythagorean identities
sin
2
θ
+
\sin^2\theta+
sin
2
θ
+
cos
2
θ
=
\cos^2\theta=
cos
2
θ
=
1
1
1
1
+
1+
1
+
tan
2
θ
=
\tan^2\theta=
tan
2
θ
=
sec
2
θ
\sec^2\theta
sec
2
θ
1
+
1+
1
+
cot
2
θ
=
\cot^2\theta=
cot
2
θ
=
cosec
2
θ
\operatorname{cosec}^2\theta
cosec
2
θ
Double angle formulae
sin
2
θ
=
\sin2\theta=
sin
2
θ
=
2
sin
θ
cos
θ
2\sin\theta\cos\theta
2
sin
θ
cos
θ
cos
2
θ
=
\cos2\theta=
cos
2
θ
=
cos
2
θ
−
sin
2
θ
\cos^2\theta-\sin^2\theta
cos
2
θ
−
sin
2
θ
cos
2
θ
=
\cos2\theta=
cos
2
θ
=
2
cos
2
θ
−
1
2\cos^2\theta-1
2
cos
2
θ
−
1
cos
2
θ
=
\cos2\theta=
cos
2
θ
=
1
−
2
sin
2
θ
1-2\sin^2\theta
1
−
2
sin
2
θ
tan
2
θ
=
\tan2\theta=
tan
2
θ
=
2
tan
θ
1
−
tan
2
θ
\frac{2\tan\theta}{1-\tan^2\theta}
1
−
t
a
n
2
θ
2
t
a
n
θ
Addition formulae
sin
(
A
±
B
)
=
\sin\left(A\pm B\right)=
sin
(
A
±
B
)
=
sin
A
cos
B
±
cos
A
sin
B
\sin A\cos B\pm\cos A\sin B
sin
A
cos
B
±
cos
A
sin
B
cos
(
A
±
B
)
=
\cos\left(A\pm B\right)=
cos
(
A
±
B
)
=
cos
A
cos
B
∓
sin
A
sin
B
\cos A\cos B\mp\sin A\sin B
cos
A
cos
B
∓
sin
A
sin
B
tan
(
A
±
B
)
=
\tan\left(A\pm B\right)=
tan
(
A
±
B
)
=
tan
A
±
tan
B
1
∓
tan
A
tan
B
\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}
1
∓
t
a
n
A
t
a
n
B
t
a
n
A
±
t
a
n
B