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Popular >

f(x)=sin(x+40)+sin(x-40)

Solution

f (x) = sin (x + 4 0^{\circ}) + sin (x - 4 0^{\circ})

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : sin (\frac{31 π}{18}) + sin (\frac{23 π}{18}) \leq f (x) \leq sin (\frac{13 π}{18}) + sin (\frac{5 π}{18})

X Intercepts : (2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{2} + 2 πn, sin (\frac{13 π}{18}) + sin (\frac{5 π}{18})), Minimum (\frac{3 π}{2} + 2 πn, sin (\frac{31 π}{18}) + sin (\frac{23 π}{18}))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [sin (\frac{31 π}{18}) + sin (\frac{23 π}{18}), sin (\frac{13 π}{18}) + sin (\frac{5 π}{18})]

Solution steps

Convert

40

degrees to radians:

\frac{2 π}{9}

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9})

Periodicity of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) : 2 π

Domain of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) : - \infty < x < \infty

Range of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) : sin (\frac{31 π}{18}) + sin (\frac{23 π}{18}) \leq f (x) \leq sin (\frac{13 π}{18}) + sin (\frac{5 π}{18})

Axis interception points of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) :

None

Extreme Points of

sin (x + \frac{2 π}{9}) + sin (x - \frac{2 π}{9}) :

Maximum

(\frac{π}{2} + 2 πn, sin (\frac{13 π}{18}) + sin (\frac{5 π}{18})),

Minimum

(\frac{3 π}{2} + 2 πn, sin (\frac{31 π}{18}) + sin (\frac{23 π}{18}))

Popular Examples

p(x)=-(-2x+3)^2

p (x) = - (- 2 x + 3)^{2}

f(y)=y^4+4y^2+5

f (y) = y^{4} + 4 y^{2} + 5

y=log_{3}(log_{5}(x))

y = lo g_{3} (lo g_{5} (x))

y = - x^{3} + 2 x

f(t)=(25)/(2t^3-75t^2)

f (t) = \frac{25}{2 t ^{3} - 75 t ^{2}}

Frequently Asked Questions (FAQ)

What is the f(x)=sin(x+40)+sin(x-40) ?
The f(x)=sin(x+40)+sin(x-40) is