Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Complete the statements below, simplify all ratios and keep them as improper fractions. If cos(θ) = and sin(θ) is negative, then sin(θ) = and tan(θ) = .

Question:

If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___  and tan(θ) =___.

Step-by-step explanation:

Given

cos(θ) =-8/17

Required

sin(θ) = __

tan(θ) =__

The first step is to determine the length of the third side

Given that

Where Adj and Hyp represent Adjacent and Hypotenuse

By comparison

Using Pythagoras

By Substitution

Subtract 64 from both sides

Take square roots of both sides

The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such

From trigonometry

Also from trigonometry

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

"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: