![]() Ī 150° lies in the second quadrant so cos 150° is negative.ī 300° lies in the fourth quadrant so sin 300° is negative.Ĭ 235° lies in the third quadrant so tan 235° is positive. Note that this is the same as saying that tan θ equals the. You will see in the following exercise why this is the case. Between 0° and 360°, this will happen when θ = 90°, or θ = 270°. Unless cos In this case, we say that the tangent ratio is undefined. For angles that are greater than 90° we define the tangent of θ by the sine of θ to be the y-coordinate of the point P.įor acute angles, we know that tan θ =.the cosine of θ to be the x-coordinate of the point P.Since each angle θ determines a point P on the unit circle, we will define For the time being we will concentrate on positive angles between 0° and 360°. Angles measured clockwise from OA are called negative angles. We measure angles anticlockwise from OA and call these positive angles. Since the length OQ = cos θ is the x-coordinate of P, and PQ = sin θ is the y-coordinate of P, we see that the point P has coordinates From the point P on the circle in the first quadrant we can construct a right-angled triangle POQ with O at the origin and Q on the x-axis. We begin by taking the circle of radius 1, centre the origin, in the plane.
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