Inverse trig domain and range is a grade 12 math skill aligned to Common Core standard HSF.TF.B.6: understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 20 inverse trig domain and range problems our math games drill.
CCSS HSF.TF.B.620 questions in the bank
Sample questions
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Question 1easy
What is arccos(21), in degrees?
cos60∘=21 and 60∘ lies in [0∘,180∘], so arccos(21)=60∘.
Question 2easy
What is arcsin(21), in degrees?
sin30∘=21 and 30∘ lies in [−90∘,90∘], so arcsin(21)=30∘.
Question 3easy
What is arctan(1), in degrees?
tan45∘=1 and 45∘ lies in arctangent's principal range, so arctan(1)=45∘.
Question 4easy
What is the domain of arcsin(x)?
The domain of arcsin(x) is [−1,1].
Question 5easy
What is arctan(1)?
tan(4π)=1, so arctan(1)=4π.
Question 6easy
What is arccos(0), in degrees?
cos90∘=0 and 90∘ lies in [0∘,180∘], so arccos(0)=90∘.
Question 7easy
What is arcsin(1), in degrees?
sin90∘=1, the top of arcsine's range [−90∘,90∘], so arcsin(1)=90∘.