Evaluate 8(1+sin 8/3 radians)without using maths table or a calculator

Answer 1

To solve this expression without using a calculator or math table, we can use some trigonometric identities and simplifications.

First, notice that the expression contains the term "sin(8/3 radians)". We can simplify this using the following identity:

sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

In this case, we have x = 8/3 radians and y = 0 radians. Therefore, we can rewrite sin(8/3 radians) as:

sin(8/3 radians) = sin(8/3)sin(0) + cos(8/3)sin(0)

Since sin(0) = 0, this simplifies to:

sin(8/3 radians) = 0

Now, we can substitute this result into the original expression:

8(1 + sin(8/3 radians)) = 8(1 + 0) = 8(1) = 8

Therefore, the value of 8(1 + sin(8/3 radians)) is 8.