Calculus question

Question

Find θ to the nearest minute if sec θ = 1.563. Show steps.

1. 39° 43'

2. 50° 17'

3. 39° 47'

3. 50° 13'

Answer 1

If your calculator can do an inverse secant, then that should get you the correct answer. Otherwise, take the reciprocal to find the cos θ=1/1.563. To solve this you take the arccos of both sides. Then, it's just converting to minutes. An arc minute is 1/60th of a degree, so if you multiply only the decimal portion by 60, it gives you minutes.

Secθ=1.563

Cosθ=1/1.563

Arccos cosθ=arccos (1/1.563)

So θ= arccos(1/1.563)

The answer is θ=50° 13'