Decide the length of the x side according to this formula?

Question

Mandy has a problem with her sin button in her calculator. Brenda suggested that she can use the following approximation instead:

sin( a times 90 degrees) = 11a - 3a^3 / 7+ a^2

Help Mandy to decide the length of the x side using Brenda's formula. Hint (a times 90degrees = 36 degrees)

Please explain how to do it I hardly understand this

Answer 1

You can first figure out what a is.  The hint is that a * 90 = 36.  Solve this equation for a:

a * 90 = 36

a = 36/90

a = 2/5

a = 0.4

Now that you know what a is, you can plug that value into the expression 11a - 3a^3 / 7+ a^2:

sin(a * 90 degrees) = 11a - 3a^3 / 7+ a^2

sin((0.4) * 90 degrees) = [11(0.4) - 3(0.4)^3] / [7 + (0.4)^2]

sin(36 degrees) = (4.4 - 0.192) / (7 + 0.16)

sin(36 degrees) = 4.208 / 7.16

sin(36 degrees) = 0.5877

Answer 2

The problem is asking you to find sin(36°)

If 90a = 36°, then a = 36/90 = 2/5 = 0.4

Now plug that into the equation:

(11(0.4) - 3(0.4)^3 ) / (7 + 0.4²)

= (4.4 - 0.192 ) / (7 + 0.16)

= 4.208 / 7.16

= 0.5877

Answer:

sin(36°) = 0.5877