![]() ![]() ![]() I'm unsure if that solves the last problem, though plugging it into Wolfram Alpha will tell you. Degree (a right angle is 90 degrees) and gradian measure (a right angle is 100 grads) have their uses. Another good rule of thumb is that if one interpretation gives an algebraic answer, use that interpretation. Calculus is always done in radian measure. If it's unspecified and of the form $360/n$ for some integer $n$, use degrees. jensenmath.ca provides FREE lessons, worksheets, solutions, and video tutorials for all Ontario high school math courses. If it's unspecified and a $\pi$ shows up, you should assume radians. In contexts where you think your professor has simplified by opting to not use the degree symbol, some general rules of thumb can be applied. If none of the problems had been marked with a degree symbol, I might think otherwise since $42.5$ is much bigger than $2\pi$. I would guess that $42.5$ is supposed to be in radians, because everywhere else in the problem the professor has been careful to use the degree symbol, making me think its omission is deliberate. This interpretation agrees with the rules of thumb that I am about to give everywhere that it's applicable, leaving the last problem. If you have been taught the technically correct rule, definitely use it. 10 years ago For any amount of radians, whole or decimal, positive or negative, you just multiply by 180/pi to get degrees. However, humans tend to be bad at being technically correct, so if you haven't been told to use radians unless otherwise specified I would consider making contextual judgement calls. ![]() The technically correct thing to do is to assume that everything is in radians unless otherwise specified. These important facts can be seen by magnifying the unit. There are 360 degrees or 2 radians in a full turn. The ° symbol means "degrees." Any answer marked with that is definitely in degrees. The derivative of sine in radians is cosine and the derivative of cosine in radians is -sine. Radians and degrees are two alternative units for measuring angle. ![]()
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