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Trigonometry

MathTo graph this function, you start with the basic function that the given function is based on: cos(x). Let's begin by examining how cos(x) looks on the graph: Let's now double the amplitude, as...

MathI'll answer the question about tangent functions, as the questions posted right before this one will show you how to directly solve this for sine. Working with tangents is not much different from...

Math(1) The phase shift of a sine function in the form `f(x)=Asin(Bx  C) + D` is `C/B` . So, to determine the phase shift of `f(x)=1/2sin(1/5xpi)+3` , plugin `B=1/5` and `C=pi` into the formula....

MathTo get the phase shift and vertical shift, you must get the equation in the following form: `f(x) = acos(b(xphi))+ c` Where a denotes the amplitude, b denotes the factor by which we divide `2pi`...

MathHere we have a graph of sin(x) (black) and the given function (blue). Notice how its amplitude is decreased, it is stretched out horizontally, its baseline is elevated, and its intersection with...

MathL.H.S.= `(tan lambda*cos^2lambda+sin^2lambda)/sinlambda` `=(sinlambda/coslambda*cos^2lambda+sin^2lambda)/sinlambda` `=(sinlambdacoslambda+sin^2lambda)/sinlambda`...

MathGiven: `sin(pi/45x)=sqrt3/2=sin(pi/3)` `rArr (pi/45x)=pi/3` `therefore (pi/45x)=npi+(1)^n(pi/3)` (where n is an integer) `rArr 5x=pi/4npi+(1)^n*pi/3` `rArr x=((14n)pi)/20+(1)^n*pi/15`...

MathWe have a right triangle where the bottom length is 1500 feet, the hypotenuse is the distance flown by the plane, and the angle between them is 14 degrees. We know that for a right triangle, the...

MathThe loading dock's height forms one leg of a right triangle. The ramp and the ground for the hypotenuse and other leg respectively. We are told that the ramp is at a 30 degree angle. Usually...

MathThe antiderivative of a function is equivalent of the integral of that function. Therefore the antiderivative of `(x^2+2x+2)^(1/2)` with respect to `x` is equivalent to `int (x^2+2x+2)^(1/2)dx`...

MathThe definition of `cosec(phi)` is that it is equal to `1/sin(phi)` . Therefore `cosec(2pi  theta) = 1/sin(2pi  theta)` Now, remembering the sine curve we have that `sin(2pi  theta) =...

Math`cos^4Asin^4A+1=2cos^2A` First, group the first two terms and factor it. `(cos^4Asin^4A)+1=2cos^2A` `(cos^2Asin^2A)(cos^2A+sin^2A)+1=2cos^2A` Then, apply the Pythagorean identity which is...

MathYou may use the alternative method to solve for a the equation, hence, you may use factorization, such that: `sin^2 a + sin^2 a  sin a  1 = 0` You may form two groups of terms such that: `(sin^2...