If the value of cos(θ) is negative, this angle (θ) can only be in one of two quadrants; the sine quadrant or the tan quadrant. In the sine quadrant, tan(θ) must be negative, but since tan(θ) > 0, we can safely say that the angle (<span>θ) is based in the tan quadrant.
We know that cos(</span><span>θ) = - Adjacent / Hypotenuse, and in this case Adjacent = 2 and Hypotenuse = 5. Using Pythagoras' theorem, we can find the opposite side of the right angled triangle situated in the tan quadrant...
</span>Adjacent² + Opposite² = Hypotenuse²
Therefore:
2² + Opposite² = 5²
Opposite² = 5² - 2²
Opposite² = 21
Opposite = √(21)
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Now, sin(θ) must be negative, as the right angled triangle is in the tan quadrant. We also know that sin(<span>θ) = Opposite / Hypotenuse, therefore:
sin(</span><span>θ) = - [</span>√(21)]/[5]
Answer:
What is not a property of all parallelograms?
Yes, opposite sides look congruent, and that's a property. But adjacent sides don't look congruent, and that's not a property. Do the sides appear to be parallel? Yes, opposite sides look parallel (and of course, you know this property if you know the definition of a parallelogram)
Step-by-step explanation:
<h3>
Answer: Choice A</h3>
Explanation:
Choice A has the f(x) values going down on the interval -1 < x < 1 only.
Choice B appears to be decreasing over its entire domain, so we can rule this out (since we want -1 < x < 1 to be the only decreasing interval).
Choice C's table isn't decreasing when -1 < x < 1 since y = -3 increases to y = 0 (from x = -1 to x = 0). So we can rule it out.
A similar situation happens with choice D as well, so we can rule this out. The function isn't decreasing when we go from f(-1) to f(0).
