Example: Intersection of sine and cosine | Graphs of trig functions | Trigonometry | Khan Academy | Summary and Q&A

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March 26, 2018
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Example: Intersection of sine and cosine | Graphs of trig functions | Trigonometry | Khan Academy

TL;DR

The graphs of y=sin(theta) and y=cos(theta) intersect twice between 0 and 2pi.

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Questions & Answers

Q: How many times do the graphs of sine and cosine intersect between 0 and 2pi?

The graphs of sine and cosine intersect twice between 0 and 2pi.

Q: What are the coordinates of the points where the graphs intersect?

The first intersection point is approximately (sqrt(2)/2, sqrt(2)/2), and the second intersection point is approximately (-sqrt(2)/2, -sqrt(2)/2).

Q: What are the values of cosine and sine at theta=0?

At theta=0, cosine is equal to 1 and sine is equal to 0.

Q: What are the values of cosine and sine at theta=pi/2?

At theta=pi/2, cosine is equal to 0 and sine is equal to 1.

Summary & Key Takeaways

  • The graph of y=cos(theta) intersects the y-axis at 1 (theta=0) and -1 (theta=pi and 2pi), forming a curve that oscillates between these points.

  • The graph of y=sin(theta) intersects the x-axis at 0 (theta=0 and 2pi) and 1 (theta=pi), forming a similar oscillating curve.

  • Between 0 and 2pi, the two graphs intersect at two points, approximately between 0 and pi/2 and between pi and 3pi/2.

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