Domain and range of a scaled inverse tangent and exact sums of two inverse tangents
Domain and range of a scaled inverse tangent and exact sums of two inverse tangents
IB Year 6 | Grade 12
7 marks
- State the domain and the range of the function \(\mathrm{f}(x)=2\arctan x\).[2]
- Find the exact value of \(\arctan\dfrac14+\arctan\dfrac35\).[3]
- Find the exact value of \(\arctan2+\arctan3\).[2]
Solution:
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Answer:(a) domain \(x\in\mathbb{R}\), range \(-\pi<\mathrm{f}(x)<\pi\) (b) \(\dfrac{\pi}{4}\) (c) \(\dfrac{3\pi}{4}\)
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