Find the zeros of the function in the interval. [-2π, 2π]

The zeroes of the f(x) = ± π/4 , ±3π/4 , ±5π/4 , ±7π/4 ⇒ answer (d)

Step-by-step explanation:

* The domain of the function f(x) = 1/2 cos(2x) is [-2π , 2π]

* That means -2π ≤ x ≤ 2π

∴ The domain of 2x is ⇒ -4π ≤ 2x ≤ 4π

* lets solve for 2x and then find the values of x

∵ f(x) = 1/2 cos(2x)

∴ The zeroes of the function means f(x) = 0

∴ 1/2 cos(2x)  = 0 ⇒ multiply both sides by 2

∴ cos(2x) = 0

* In the four quadrant the values of cosФ = 0 at the y-axis with angles

  π/2 , 3π/2 (anti-clockwise) , -π/2 , -3π/2 (clockwise) for 1 cycle,

  but we have 2 cycles for 2x, so we add 2π for every angle of

  2x, then we have other 4 angles 5π/2 , 7π/2 (anti-clockwise),

  -5π/2 , -7π/2 (clockwise)

∴ 2x = ± π/2 , ±3π/2 , ±5π/2 , ±7π/2

* To find the value of x divide all by 2

∴ x = ± π/4 , ±3π/4 , ±5π/4 , ±7π/4

* The zeroes of the f(x) = ± π/4 , ±3π/4 , ±5π/4 , ±7π/4

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: