Describe the relationship between the unit circle and tangent.
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Given that $${\mathrm{cos\theta}=\frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}}$$and $${\mathrm{sin\theta}=\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}}$$, what is the definition of $${\mathrm{tan\theta}}$$ in terms of sine and cosine?
What is the slope of the line containing $${\overline{AD}}$$?
Show how you determine this using the trigonometric ratios for ANY angle.
Below is a diagram with a line segment tangent to the circle at point $$E$$. $$\bigtriangleup ABC\approx \bigtriangleup ADE$$. The radius of the circle is $$1$$.
What is the value of $$\overline{DE}$$ in terms of trigonometric ratios?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Draw and label a figure on the circle that illustrates the relationship of the trigonometric tangent functions $${\mathrm{tan}=\frac{\mathrm{sin}(\theta^\circ)}{\mathrm{cos}(\theta^\circ)}}$$ and the geometric tangent line to a circle through the point $${(1,0)}$$ when $${\theta=60}$$. Explain the relationship, labeling the figure as needed.
Algebra II > Module 2 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..