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Derive Law of Cosines using Pythagorean Theorem

Consider the triangle ABC. Denote h the altitude through B and D the point where h intersects the (extended) base AC Cosine function for triangle ADB. cos α= x/c => x=c*cos α Pythagorean theorem for trian...
JM
Answered by Jan M. • Maths tutor
3861 Views

Given that Sin(A) = 1/sqrt(3), show that Tan(A) = 1/sqrt(2)

Using: Tan(x) = Sin(x)/Cos(x) Using: Cos(x) = sqrt(1-Sin 2 (x)) Cos(A) = sqrt(1-Sin 2 (A)) = sqrt(1-1/3) = sqrt(2)/sqrt(3) Therefore: Tan(A) = Sin(A)/Cos(A) = (1/sqrt(3))/(sqrt(2)/sqrt(3)) = 1/sqrt(2)
SH
Answered by Sameh H. • Maths tutor
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What is the "chain rule"?

The "chain rule" is a handy little tool that we can use to find the derivative of a complicated function. Specifically, we use the chain rule when we have functions within functions. But what does ...
JF
Answered by Joe F. • Maths tutor
4294 Views

2+2 is 4, minus 1, that's what?

Quick maths.
JF
Answered by Joe F. • Maths tutor
4898 Views

Find the values of the constants a and b for which ax + b is a particular integral of the differential equation 2y' + 5y = 10x. Hence find the general solution of 2y' + 5y = 10x .

We start by letting yp = ax+b, as suggested, and finding the derivative yp' = a. Substituing into ODE (by way of matching coefficients) gives a pair of simulataneous (algebraic) equations: (1) 2a=5b (2) -5a=...
BR
Answered by Ben R. • Maths tutor
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