Mini problem

Geometry Level 2

$\cos\left[\sin^{-1}\left(\frac{-7}{11}\right)+\sec^{-1}\left(\frac{-11}{7}\right)\right]$

Evaluate the expression above.

The answer is 0.00.

1 solution

Vishnu Bhagyanath
May 17, 2015

$cos [ sin^{-1}(\frac{-7}{11}) + sec^{-1}(\frac{-11}{7})]$ $cos [ sin^{-1}(\frac{-7}{11}) +cos^{-1}(\frac{-7}{11})]$ $cos [\theta + (90-\theta)]$ $=cos(90) = 0$

Moderator note:

Careful there, you're implying that $sin^{-1}(\frac{-7}{11}) = \theta$ and $cos^{-1}(\frac{-7}{11}) = 90 - \theta$ . Checking with a scientific calculator shows that they don't satisfy both equations at the same time.

Do you know why? Because you have committed a fallacy. Can you find what fallacy that is?

How did you consider them as complementary angles?

Sameer Alam - 4 years ago

To challenge master: If we let $\theta = -\sin^{-1}\frac{7}{11}$ , then everything checks out. Could you explain what the fallacy is? I don't understand.

John Frank - 3 years, 9 months ago

Mini problem

The answer is 0.00.

1 solution

Moderator note:

0 pending reports