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Welcome to NRICH.
Trigonometrical, exponential and logarithmic functions
For trigonometry and triangles, see under
Shape and geometry
Trigonometric functions
5
Trigonometric Inequality
5
Period and frequency of trig functions
5
Minimum of 1/(2cos4x+3sin4x)
5
Proving tan(x)=-tan(-x)
5
cos(i)=cosh(1)
5
Trig functions with complex variables
5
Exact calculation of sines, cosines and angles
5
Exact Values of Trigonometric Functions
5
cos(7
p
/12) in surd form
5
Surd form of tan(3
p
/8)
5
cos(
p
/8)
5
Sin(pi/10) as a surd expression
5
Definition of Cosine
6
Rational Cosine
5
Cos(m) Irrational
5
What is sin 10
40
?
Trigonometric identities and equations
4
Generate Trigonometric Identities
5
Intersection of y=tan x and y=cos x
5
tan(
q
) = 1 ± 2
0.5
5
tan(3x)=tan(x)
5
sin
q
-cos
q
5
Deriving sinA+sinB formula
5
2cos3xcosx = cos2C + cosC
5
3sinx + 4cosx + 3 = 0
5
Prove tan(4pi/11)+4sin(pi/11)=sqrt(11)
5
Solve cos2x-cos4x=sin2x
5
<<A HREF=../2886.html >Trigonometric Identities
5
Expansion of tan(A+B)
5
Solve sin6x-sin4x=sin5x-sin3x
5
sin(x+a)=sqrt(2)cos(x-a): find tan(x)
5
Manipulating trig expressions
5
Questions about roots of x
2
+ 2xsin
q
+ 3cos
2
q
= 0
5
cos
3
q
=sin
q
5
cos(sinx) > sin(cosx)
Hyperbolic functions and identities
5
Trig identity to hyperbolic identity
5
Hyperbolic Trigonometrical Functions
5
Hyperbolic question
5
tanh(2x)
5
ò
Cosh
2
x dx and hyperbolic identities
5
Inverse hyperbolics in logarithmic form
5
tanh
2
(x/2)=(cosh(x)-1)/(cosh(x)+1)
Exponentials and logarithms
4
Solving equations such as 7
x
=343
5
Definition of y
x
for irrational x
5
Solving log equations
5
Manipulating logs
5
Logs puzzle
5
Exponential growth problem
5
Hyperbolic functions, natural logarithms and complex numbers
5
Inverse hyperbolics in logarithmic form
5
Inx (or ln x)
5
e
5
ln2 = 0: series paradox?
6
log(1)+log(2)+log(3)+...
Series expansions
5
Proving MacLaurin's theorem
5
Maclaurin's series don't always work...?
5
Maclaurin series for tan(x), and polynomial division
5
Binomial Expansion: (1 + px + qx
2
)
-2
5
Binomial Theorem to find 1.1
6
5
Series for trigonometric functions and e
x
5
Trigonometric Power Series
5
Pi's value as an infinite series
5
Infinite Series for Sine and Cosine
5
Exact calculation of sines, cosines and angles
5
Maclaurin series for sin
2
x
5
Series for 1/sin(x)
5
A Logarithmic Series
5
Log Power Series
5
Series expansion for cos
-1
x
5
cos(
q
)+ cos(3
q
) + cos(5
q
)+....+ cos(2n-1)
q
= sin(2n
q
)/sin(
q
)
5
Coefficient of x
34
in expansion of (1-3x+x
2
+2x
4
)
10
6
Reconciling definitions of sine
Applications
5
Triangle right-angled iff a
2
+b
2
+c
2
=8R
2
4
Distance of horizon from leaning tower
5
Motivate project:
The sun
Miscellaneous
5
S
n
r=0
sin((2n+1)x/4)
5
Show arsinh(x) is approx ln2 + lnx + 1/4x
2
6
Fourier transforms
6
lim
n->
¥
sin(cos(sin(cos(sin(cos(......ntimes....(0)))).....)