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Why does cos negative theta equals positive theta?
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
How do you prove that 2 sin 3x divided by sin x plus 2 cos 3x divided by cos x equals 8 cos 2x?
You need to know the trigonometric formulae for sin and cos of compound angles. sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y) and cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) Using these, y = x implies that sin(2x) = sin(x+x) = 2*sin(x)cos(x) and cos(2x) = cos(x+x) = cos^2(x) - sin^2(x) Next, the triple angle formulae are: sin(3x) = sin(2x + x) = 3*sin(x) - 4*sin^3(x) and cos(3x) = 4*cos^3(x) - 3*cos(x) Then the left hand side = 2*[3*sin(x) - 4*sin^3(x)]/sin(x) + 2*[4*cos^3(x) - 3*cos(x)]/cos(x) = 6 - 8*sin^2(x) + 8cos^2(x) - 6 = 8*[cos^2(x) - sin^2(x)] = 8*cos(2x) = right hand side.
If tan y equals to x where y is acute find 3 cos y in terms of x?
3cos(y) = 3/(sqrt(1+x^2)
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
6 trigonometric values of 315 degrees?
To find exact values, you should use the unit circle.It is good practice, too, to use radians as this is much more helpful in higher levels of math, so, do yourself a favor and learn how to convert degrees into radians and start thinking about the circle in radians instead of degrees.315 degrees = (7 [Pi])/4 radiansYou can use the following conversion to find this: 90 degrees = Pi / 2 radians.315 / 90 = x / (Pi / 2), solve for x.Although you can find decimal approximations using a calculator, it is better to find these on the unit circle and start building your knowledge about radians and how they related to each other and the circle. You will soon find out that most of the time you are dealing with a 3, 4, 5 or right triangle.Turns out that here we are looking at the right triangle in the 4th quadrant of the unit circle. All angles in the 4th quadrant share certain principles. x is positive and y is negative in the 4th quadrant. This means that cos is going to be positive and sin and tan are going to be negative. All right triangles also have similar properties, their sin and cos are going to be equal or differ only by their sign and will be either Sqrt(2)/2 or -Sqrt(2)/2.Building this intuitive knowledge about the unit circle and the angles it contains will serve you much better than getting decimal approximations.sin( (7 [Pi])/4 ) = -1/Sqrt(2) = -Sqrt(2)/2cos( (7 [Pi])/4 ) = 1/Sqrt(2) = Sqrt(2)/2To find tangent, you need to do a little arithmetic. We know that tan(x) = sin(x) / cos(x), so,tan( (7 [Pi])/4 ) = sin( (7 [Pi])/4 ) / cos( (7 [Pi])/4 ) = (-Sqrt(2)/2)/(Sqrt(2)/2) = -1You can also remember that this is a right triangle and tangent is also going to be 1 or -1 depending on the quadrant.The cossec, sec and cot values are the reciprocals of these values:cossec( (7 [Pi])/4 ) = 1/sin( (7 [Pi])/4 ) = 1/(-Sqrt(2)/2) = -Sqrt(2)sec( (7 [Pi])/4 ) = 1/cos( (7 [Pi])/4 ) = 1/(Sqrt(2)/2) = Sqrt(2)cot( (7 [Pi])/4 ) = 1/tan( (7 [Pi])/4 ) = cos( (7 [Pi])/4 ) / sin( (7 [Pi])/4 ) = -1
What is the derivative of cos pi x plus sin pi y all to the 8th power equals 44?
(cos(pi x) + sin(pi y) )^8 = 44 differentiate both sides with respect to x 8 ( cos(pi x) + sin (pi y ) )^7 d/dx ( cos(pi x) + sin (pi y) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (-sin (pi x) pi + cos (pi y) pi dy/dx ) = 0 8 ( cos(pi x) + sin (pi y ) )^7 (pi cos(pi y) dy/dx - pi sin (pi x) ) = 0 cos(pi y) dy/dx - pi sin(pi x) = 0 cos(pi y) dy/dx = sin(pi x) dy/dx = sin (pi x) / cos(pi y)
Find the equation of the line tangent to the graph of y equals cos2x at x equals pi divided by 4?
0.5
What is x equals y squared over co sign times pi?
Either you mean "cos(x) multiplied by pi", (i.e pi*cos(x)) or "cos(pi)" (i.e cosine of pi), but it is unclear which you mean from the question. Please clarify.
What is the equation of the line tangent to the curve y equals cos x at the point x equals pi over 6?
y = 2(x) - (pi/3) + (sqrt(3)/2)
Y equals 4 sin x for x equals pi?
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
What is the range of y equals arc cos x?
It is pi radians wide. The end point is arbitrary.
What is x equal y sq over cos x pi?
Can you please claify if you mean x=y^2/ pi*cos(x) , or x=y^2/cos(pi), since they are very different sums.
What is the range for y equals 4 cos parantheses2xparantheses?
The range for y = 4 cos (2x) is [-4, +4].Not asked, but answered for completeness sake, the domain is [-infinity, +infinity].
Why does cos negative theta equals positive theta?
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
How do you solve cos squared x - cosx equals 2 for 0x2pi?
cos2(x) - cos(x) = 2 Let y = cos(x) then y2 - y = 2 or y2 - y - 2 = 0 factorising, (y - 2)(y + 1) = 0 that is y = 2 or y = -1 Substitutng back, this would require cos(x) = 2 or cos(x) = -1 But cos(x) cannot be 2 so cos(x) = -1 Then x = cos-1(-1) => x = pi radians.
If Sin equals x and Cos equals y then x squared equals what function of y?
If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
What is sin23A minus sin7A upon sin2A plus sin14A if A equals pi upon 21?
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
