What is the value of a

Question

If the following function is continuous what is the value of a

h(t) = {2t+b if t<0 }

{ 2cos(t) -3 if 0≤t≤ π/2}

{ asin(t) + 5b if t>π/2}

I know you set everything equal to each other to solve this but Im not sure how to handle the trig functions

Answer 1

What you need to do is set the curves equal at the end points.

The first two equations match up when t = 0

2t+b =2cos(x)-3

b = 2(1) -3 = -1

The second and third equations match up when t = π/2

2cos(t)-3 = asin(t)+5b

2(0)-3 = a(1)-5

a = -2

Answer 2

desmos.com/calculator/pgthpikob5

Visit the above graph and click the Make Continuous link to make h(t) a continuous function at x = 0 and x = pi/2.