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:
A, D, F
Step-by-step explanation:
Angle BAC is angle A in triangle ABC. Use the definitions of the trigonometric functions:
[tex]\cos \angle A=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{AC}{AB}=\dfrac{6.9}{12}\\ \\\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{9.8}{12}\\ \\\tan \angle A=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{BC}{AC}=\dfrac{9.8}{6.9}\\ \\\cot \angle A=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{AC}{BC}=\dfrac{6.9}{9.8}[/tex]
Now
[tex]\angle A=\cos^{-1}\left(\dfrac{6.9}{12}\right)\\ \\\angle A=\sin^{-1}\left(\dfrac{9.8}{12}\right)\\ \\\angle A=\tan^{-1}\left(\dfrac{9.8}{6.9}\right)\\ \\\angle A=\cot^{-1}\left(\dfrac{6.9}{9.8}\right)[/tex]
So, correct options are A, D and F