Question

18sin117градус•cos117градус/sin234градус

Answer 1

$\frac{18 \sin(117) \times \cos(117) }{ \sin(234) } = \frac{9 \times 2 \sin(117) \cos(117) }{ \sin(234) } = \\ = \frac{9 \sin(234) }{ \sin(234) } = 9$

Answer 2

To evaluate the expression, we need to convert the angles from degrees to radians because trigonometric functions typically operate in radians. The conversion formula is:

Radians = Degrees × π / 180

Let's calculate it step by step:

1. Convert the angles to radians: 117 degrees = 117 × π / 180 radians ≈ 2.04203522483 radians 234 degrees = 234 × π / 180 radians ≈ 4.08407044965 radians

2. Calculate the trigonometric values: sin(117 degrees) ≈ sin(2.04203522483 radians) ≈ 0.88192126435 cos(117 degrees) ≈ cos(2.04203522483 radians) ≈ 0.47139673683 sin(234 degrees) ≈ sin(4.08407044965 radians) ≈ -0.37460659342

3. Substitute the values into the expression: (18 * sin(117 degrees) * cos(117 degrees)) / sin(234 degrees) = (18 * 0.88192126435 * 0.47139673683) / (-0.37460659342) ≈ (-7.9729700583) / (-0.37460659342) ≈ 21.2915851516

So, the result of the expression is approximately 21.29.