Sin/Cos

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I'm having trouble with a concept. I don't understand how the answer was found.

1. Find three other angles, such that cos[beta] = cos [25].
Answers are -25, 335, -335.

In my Calc class, the teacher showed it by using a circle, with an angle. Can anyone please help me, via links or some explanation?

I would also appreciate it if an explanation was provided for sine.

1. Three other angles for
sin[beta] = sin[-65]
Answers are 295, -115, and 245.

  • Sin/Cos -

    You are using reference angles for this.

    Where is cosine the same? Cosine in Quadrants I & IV because cosine (referring to the x-coordinate) is positive there. It is negative in Quadrants II & III.

    Negative angles are simply the angle backtracked from standard position (0 or 360 degrees). It is helpful to draw a circle for these problems.

    For the first one, cos(25) is the same as cos(-25) because 25 degrees is in Q1 and -25 degrees is in Q4, so the cosine value is the same.

    We can also get the same two angles by adding 360 to -25 and subtracting 360 from 25.

    For this type of problem, it is easiest to (1) recall in which quadrants sine or cosine is equivalent, (2) determine an in the other quadrant that gives an equivalent sine or cosine value, and (3) either adding or subtracting 360 to get angles that are equivalent to the given angle and to the angle you found in step 2.

    If you have any questions, just ask.

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