Question

(5*sin(74°))/(cos(37°)*cos(53°))

Answer 1

Разлаживаем sin74° как синус двойного аргумента sin2L = 2sinLcosL. Затем скорачиваем cos37°. Потом представлеям cos53=sin(90-37)=sin37 (за формулами привидения). Скорачиваем sin37.

 

 (5*sin(74°))/(cos(37°)*cos(53°) )= (5*2*sin37°cos37°))/(cos(37°)*cos(53°)) =10*sin37°/cos53° = 10**sin37°/sin37 = 10.

 

Ответ: 10.

Answer 2

To calculate the value of the expression (5*sin(74°))/(cos(37°)*cos(53°)), we can use a scientific calculator or mathematical software. However, I can also provide you with the approximate result using the available information. Please note that the following calculation assumes angle measurements are in degrees:

First, let's calculate the individual trigonometric functions:

sin(74°) ≈ 0.9613 (rounded to four decimal places) cos(37°) ≈ 0.7986 (rounded to four decimal places) cos(53°) ≈ 0.6008 (rounded to four decimal places)

Now, let's substitute these values into the expression:

(5*sin(74°))/(cos(37°)*cos(53°)) ≈ (5 * 0.9613) / (0.7986 * 0.6008) ≈ 4.8065 / 0.4797 ≈ 10.0191

Therefore, the approximate value of the expression is 10.0191.