Question

Hi am really stuck on this question.

find the equation of the tangent to the following curves at the point indicated.

y= 3cos x - 2sin x where x=π/4

i have the right method but finding it hard to simplify the answer to 5x+√2*x-1-5π/4=0 (the x is multiplied by square root of 2)

I have differentiated the function and inserted x=π/4 to get the gradient.
i have then tried to find the value of y by putting x=π/4 into the original equation
y=3cos x - 2sin x

the bit i am stuck in is finding the equation by using the gradient formula y-y(1)/x-x(1)=m.
can you help me please to get t

Answer 1

f(x) = 3cos x - 2sin x
-> f'(x) = -3 sinx - 2cosx
=> f'(π/4) = - 5 √2/2
Tangent line at x = π/4:
y = - 5 √2/2 ( x - π/4 ) + √2/2
= -√2/2 ( 5x - 5π/4 - 1 )
-√2y = 5x - 5π/4 - 1
0 = √2y + 5x - 5π/4 - 1

Answer 2

thanks very much i really appreciate the reply cheers.