If P\left(x,\ -\dfrac{\sqrt{2}}{3} \right) is a point on the unit circle that x \gt 0, find \tan...
Question:
If {eq}P\left(x,\ -\dfrac{\sqrt{2}}{3} \right) {/eq} is a point on the unit circle that {eq}x \gt 0 {/eq}, find {eq}\tan \theta {/eq}, where {eq}P {/eq} is on the terminal side of the angle of {eq}\theta {/eq} radians.
Unit circle: definition and tangent function:
Definition:
The unit circle is the circle with radius 1 centered at the origin. That is, in Geometry, the set of all points that lies on a plane whose distance from the origin is less than 1(or equal to 1).
Standard form equation of the unit circle:
The standard form equation of the unit circle is presented below:
{eq}x^2+y^2=1 {/eq}
Tangent function:
We can find the tangent function of the angle {eq}\theta {/eq} with vertex at the origin and whose terminal side intersects the unit circle at the point {eq}P(x,y) {/eq}, using the corodinates of this point:
{eq}\tan\theta=\dfrac{y_P}{x_P} {/eq}
Answer and Explanation: 1
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View this answerWe are given the y-coordinate of a point {eq}P {/eq} lying on the unit circle. We must find the tangent of the angle with vertex at the origin whose...
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Chapter 11 / Lesson 1Learn about the unit circle in trigonometry. Understand the use of the unit circle to find the trigonometric functions. See how to find sine and cosine from a unit circle and how to find the tangent using unit circle sine-cosine ratios.