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

Answer:

A, D, F

Step-by-step explanation:

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

$\cos \angle A=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{AC}{AB}=\dfrac{6.9}{12}\\ \\\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{9.8}{12}\\ \\\tan \angle A=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{BC}{AC}=\dfrac{9.8}{6.9}\\ \\\cot \angle A=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{AC}{BC}=\dfrac{6.9}{9.8}$

Now

$\angle A=\cos^{-1}\left(\dfrac{6.9}{12}\right)\\ \\\angle A=\sin^{-1}\left(\dfrac{9.8}{12}\right)\\ \\\angle A=\tan^{-1}\left(\dfrac{9.8}{6.9}\right)\\ \\\angle A=\cot^{-1}\left(\dfrac{6.9}{9.8}\right)$

So, correct options are A, D and F

Answer 2

Answer:

1,4,6 or A,D,F

Step-by-step explanation: