Nataly M.

# Find all solutions to equation sin t - cos t = 1

express results in radians

## 2 Answers By Expert Tutors

By:

William W. answered • 02/02/20

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Experienced Tutor and Retired Engineer

Marc N.

tutor
Simply because two functions f and g share the range [-1,1], we cannot conclude that solutions of f(t) - g(t) = 1 result in the form 1 - 0 or 0 - (-1). For example, consider the equation sin(2t) - cos t = 1. The two terms still have range [-1,1], but in addition to the solutions t = (2k+1)π, we have t = 2πk + 4.357 (approximately) even though neither sin(2t) nor cos t is +1/-1/0.
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03/03/20

William W.

tutor
You are correct generally. I was speaking specifically about sin(x) and cos(x). My apologies for the wording of my answer.
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03/03/20

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