Question

Which expressions can be used to find m∠BAC? Check all that apply. cos−1 cos−1 sin−1 sin−1 tan−1 tan−1

Answer 1

1,4,6 or A,D,F

Explanation:

Answer 2

A, D, F

Explanation:

Angle BAC is angle A in triangle ABC. Use the definitions of the trigonometric functions:

`\cos \angle A=\frac{\text{adjacent leg}}{\text{hypotenuse}}=(AC)/(AB)=(6.9)/(12)\\ \\\sin \angle A=\frac{\text{opposite leg}}{\text{hypotenuse}}=(BC)/(AB)=(9.8)/(12)\\ \\\tan \angle A=\frac{\text{opposite leg}}{\text{adjacent leg}}=(BC)/(AC)=(9.8)/(6.9)\\ \\\cot \angle A=\frac{\text{adjacent leg}}{\text{opposite leg}}=(AC)/(BC)=(6.9)/(9.8)`

Now

`\angle A=\cos^(-1)\left((6.9)/(12)\right)\\ \\\angle A=\sin^(-1)\left((9.8)/(12)\right)\\ \\\angle A=\tan^(-1)\left((9.8)/(6.9)\right)\\ \\\angle A=\cot^(-1)\left((6.9)/(9.8)\right)`

So, correct options are A, D and F