Do all perpendicular lines have negative reciprocal slopes?

Mathematics

1 answer:

inna [77]3 years ago

6 0

Not necessarily, the more correct definition is opposite reciprocal slopes.

The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.

In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.

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9. You need an exact answer. So I will give you it but I'll also give you an approximation because it might help you understand it more.

Because we know the cosine fo theta, we can evaluate the inverse cosine of -2/3 first to find theta.

$sin^{-1}(-2/3)$ = 131.81° approx.

Because 131.81° is in the second quadrant its third quadrant partner is 228.19°. Which would make the sine 0.75 approximately.

But we need an exact answer I suppose so which is this disgusting mess... $sin(2\pi -cos^{-1}(\frac{-2}{3}))$ . I know it looks scary but it is basically all the steps we just did but without evaluating anything.