For the given triangle, the slope of ZX is 1/3, the slope of ZY is -1/2, and the slope of XY is 2. Which statement verifies that
2 answers:
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Answer: A. The value of his investment decreased by 16% during this time period.
Step-by-step explanation:
Here the initial amount = n
Final amount after 1 years = 0.84n
The total change in the initial amount = n - 0.84n = 0.16 n
=
Thus, the amount is decreases by 16% in one year,
⇒ Option A is correct.
Recall that sine is the ratio of opposite over hypotenuse, so we say
sin(theta) = opposite/hypotenuse
If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C
Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.
Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.
So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.
Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.
