Given 𝑦 = cos−1(0.4), find the exact values of sec y, sin 𝑦 and tan 𝑦

Sure, let's solve this step by step.

Step 1: We know that y = cos^(-1)(0.4). This means that cos(y) = 0.4.

Step 2: We can find sec(y) by taking the reciprocal of cos(y). So, sec(y) = 1/cos(y) = 1/0.4 = 2.5.

Step 3: To find sin(y), we can use the Pythagorean identity sin^2(y) + cos^2(y) = 1. Solving for sin(y), we get sin(y) = sqrt[1 - cos^2(y)] = sqrt[1 - 0.4^2] = sqrt[0.84] = 0.916515138991168.

Step 4: Finally, to find tan(y), we can use the identity tan(y) = sin(y)/cos(y). Substituting the values we found, we get tan(y) = 0.916515138991168/0.4 = 2.291287847478.

So, the exact values of sec y, sin y, and tan y are 2.5, 0.916515138991168, and 2.291287847478 respectively.