Grade 12 · Algebra & functions

Inverse trig domain and range practice

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

Try 8 for free

Question 1easy

What is arccos(12)\arccos\left(\dfrac{1}{2}\right), in degrees?

cos60=12\cos 60^{\circ} = \dfrac{1}{2} and 6060^{\circ} lies in [0,180][0^{\circ}, 180^{\circ}], so arccos(12)=60\arccos\left(\dfrac{1}{2}\right) = 60^{\circ}.

Question 2easy

What is arcsin(12)\arcsin\left(\dfrac{1}{2}\right), in degrees?

sin30=12\sin 30^{\circ} = \dfrac{1}{2} and 3030^{\circ} lies in [90,90][-90^{\circ}, 90^{\circ}], so arcsin(12)=30\arcsin\left(\dfrac{1}{2}\right) = 30^{\circ}.

Question 3easy

What is arctan(1)\arctan(1), in degrees?

tan45=1\tan 45^{\circ} = 1 and 4545^{\circ} lies in arctangent's principal range, so arctan(1)=45\arctan(1) = 45^{\circ}.

Question 4easy

What is the domain of arcsin(x)\arcsin(x)?

The domain of arcsin(x)\arcsin(x) is [1,1][-1,\, 1].

Question 5easy

What is arctan(1)\arctan(1)?

tan ⁣(π4)=1\tan\!\left(\dfrac{\pi}{4}\right) = 1, so arctan(1)=π4\arctan(1) = \dfrac{\pi}{4}.

Question 6easy

What is arccos(0)\arccos(0), in degrees?

cos90=0\cos 90^{\circ} = 0 and 9090^{\circ} lies in [0,180][0^{\circ}, 180^{\circ}], so arccos(0)=90\arccos(0) = 90^{\circ}.

Question 7easy

What is arcsin(1)\arcsin(1), in degrees?

sin90=1\sin 90^{\circ} = 1, the top of arcsine's range [90,90][-90^{\circ}, 90^{\circ}], so arcsin(1)=90\arcsin(1) = 90^{\circ}.

Question 8easy

What is arctan(0)\arctan(0), in degrees?

tan0=0\tan 0^{\circ} = 0, so arctan(0)=0\arctan(0) = 0^{\circ}.

Drill it inside a game.

The free placement test finds your level, then every match serves inverse trig domain and range questions at exactly the right difficulty.