Question - Understanding Inverse Trigonometric Functions
Solution:
The question in the image asks to evaluate the expression:\[ \cos(\cos^{-1}(-0.9)) \]By definition, the inverse cosine function, $$\cos^{-1}(x)$$, returns the angle whose cosine is $$x$$. Therefore, when we apply the cosine function to the result of an inverse cosine function, we get back the original value inside the inverse cosine.For the given problem:\[ \cos(\cos^{-1}(-0.9)) = -0.9 \]This is because the inverse cosine of $$-0.9$$ gives us the angle whose cosine is $$-0.9$$, and taking the cosine of that angle returns us back to the original value of $$-0.9$$.So the correct answer is:-0.9
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