Question

Which angle between 0° and 360° has the same cosine as the angle 63°?

Enter your answer as an integer

Answer 1

Answer on Question#54404 – Math – Trigonometry

1. Which angle between $0{}^{\circ}$ and $360{}^{\circ}$ has the same cosine as the angle $63{}^{\circ}$? Enter your answer as an integer.

Solution.

We know that cosine is positive in first and forth quadrants. Angle $63{}^{\circ}$ is located in first quadrant and $\cos 63{}^{\circ}$ is positive. Hence, another angle which has the same cosine is located in forth quadrant. We can write next identity:

$\cos(360{}^{\circ} - \alpha) = \cos \alpha$, where $\alpha < 90{}^{\circ}$. It derived from the fact that we have the same value of cosine, when we move counterclockwise and clockwise in unit circle.

So, in our case we have:

$$360{}^{\circ} - 63{}^{\circ} = 297{}^{\circ}.$$

Answer:

hence, $\alpha = 297{}^{\circ}$

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