Approximate the value of cos((𝜋)+0.06) using a tangent line approximation.

Question

cos((𝜋/2)+0.09)=

Answer 1

Hello Blaise R.,

I will start you off on the first one. You find a simple value close to the one they ask. Now cos (p1/2) = 0 and that is very close to cos (pi/2 + 0.09). Then find the tangent line for y = cos(x) at (pi/2, 0). This line will have

y = mx + b where m is the slope (derivative in calculus). The slope formula for y is y ' = -sin(x). Find that value at x = pi/2 and that will be m. To find b, substitute the point (pi/2, 0) into the y = mx + b equation and find b.

Once you have the tangent line with the correct m and b, simply substitute x = (pi/2 + 0.09) into your line equation to get the answer. See if you can write the rest of that one. Then try the same method on the other problem.

Tom S.