Question

In: Other

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?

enter image source here

Expert Solution

See below.

Explanation:

Form the diagram:

By Pythagoras's theorem:

#PO^2=12^2+5^2=169#

#PO=sqrt(169)=13#

#cos(y)=5/13#

#sin(x)=5/13#

The ratios are the same

This is true for all right triangles.

From diagram:

#sin(alpha)=a/c#

#cos(beta)=a/c#

#sin(beta)=b/c#

#cos(alpha)=b/c#

For all right triangles:

#sin(theta)=cos(90^@-theta)#

Amanda K answered 2 years ago

Find dy/dx by implicit differentiation: cos(x+y)=y^3 sin x

Find the general solution of the differential equations. A: cos(x)y′(x) + y(x) sin(x) = 0 B:...

Find the general solution of the differential equations. A: cos(x)y′(x) + y(x) sin(x) = 0 B: 2xy + (x2 + y2)y′ = 0 C: (4x3 +2xy2 +1)dx+(2x2y−1)dy=0. D: x(4x3 +2xy2 +1)dx+x(2x2y−1)dy=0 with steps please.

Find dy/dx for a & b a) sin x+cos y=1 b) cos x^2 = xe^y c)Let...

Find dy/dx for a & b a) sin x+cos y=1 b) cos x^2 = xe^y c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the second derivative f'' (x) equals zero. d) For what value of the constant c is the function f continuous on (−∞,∞)? f(x) = {cx^2 + 2x, x < 2 , 2x + 4, x ≥ 2}

subject:engineering mathematics solve [cos(x+y)-sin(x+y)]dx-sin(x+y)dy=0,is the ODE exact?Find an integrating factor and solve the ODE.

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line...

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line to curve when t=1

Find the solution of the initial-value problem. y'' + y = 3 + 5 sin(x), y(0)...

Find the solution of the initial-value problem. y'' + y = 3 + 5 sin(x), y(0) = 5, y'(0) = 8

Use implicit differentiation to find ∂z/∂x and ∂z/∂y if xz = cos (y + z).

Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5...

Solve the initial value problem dy/dx = −(2x cos(x^2))y + 6(x^2)e^(− sin(x^2)) , y(0) = −5 Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1 + t^6)^2 , y(1) = 8. Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y)...

The value of f depends on two independent variables x and y as defined below: f(x,y)=x2+y2−x+3cos(x)sin(y) Function f has a minimum in the neighborhood of the origin (i.e. [0 0]). Find x and y which minimize f. Note: You are not allowed to use MATLAB built-in functions for optimization. Follow the logic of the derivative test: The minimum of f occurs where: ∂f∂x=0∂f∂y=0

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0)...

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0) = 2 x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14 x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5