How do you evaluate #cos A = 0.7431#?

2 Answers
May 24, 2018

#angleA=42^@#

Explanation:

#"given "cosA=0.7431#

#"then "angleA=cos^-1(0.7431)=42^@#

May 24, 2018

#A = pm text{Arc}text{cos} (0.7431) + 360^circ k quad #integer #k#

#A approx pm 42.0038^circ + 360^circ k quad #integer #k#

Explanation:

Cosines, unlike sines, uniquely determine a triangle angle between #0# and #180^circ.#

But we're not given any such constraint here. As far as we know, #A# can be any angle, any real number of degrees or radians.

What's important to remember is the general solution to #cos x = cos a # is #x=pm a + 360^circ k ,# integer #k.#

The principal value of the inverse cosine gives us a particular solution and we apply the recipe to turn it into the general solution.

#cos A = 0.7431 = cos text{Arc}text{cos} (0.7431)#

#A = pm text{Arc}text{cos} (0.7431) + 360^circ k quad #integer #k#

That's the exact, general answer. It gives all the #A#s whose cosine is #0.7431#.

Now we're supposed to get out our calculator and evaluate the inverse cosine. I don't like that part. I got a nice exact answer here and I have to muck it up.

#A approx pm 42.0038^circ + 360^circ k quad #integer #k#