Angles, the Unit Circle and Trigonometric Graphs

Name: Angles, the Unit Circle and Trigonometric Graphs
Author: StemPy Lab

Convert between degrees and radians in code and compute sine, cosine and tangent for any angle. Then draw the unit circle, plot the graphs of the trigonometric functions, and test identities on thousands of angles at once.

3 lessons, about 1 h 40 min3 simulations11 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Degrees, radians and the unit circle
Python measures angles in radians, so degrees must be converted with math.radians. The unit circle shows that the point at an angle is (cos, sin), which fixes the signs in every quadrant. A loop builds the table of the six ratios, and a tolerance, not ==, compares the answers, since sin(pi) is not exactly zero.
1 simulation1 practice question2 Python programs4 problems1 Python lab
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Lesson 2about 35 min
Plotting sine, cosine and tangent
A table lists a few angles, and a graph shows all of them. np.linspace makes the angles, np.sin works on the whole array, and plt.plot draws the curve. The wave $y = A\sin\big(B(x - C)\big)$ has amplitude $A$ , period $\dfrac{2\pi}{B}$ and phase shift $C$ . Tangent has asymptotes, so its huge values are replaced by nan before plotting.
1 simulation1 practice question4 Python programs4 problems
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Lesson 3about 35 min
Checking identities in code
An identity is an equation that is true for every angle. A program cannot try every angle, but it can try thousands at once. np.allclose tests whole arrays within a tolerance, np.max of the absolute difference shows the worst miss, and np.argmax finds a counterexample. One failure proves an identity false, and many passes make it very likely true.
1 simulation1 practice question4 Python programs3 problems1 Python lab1 question set1 note
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Angles and the Unit Circle by Computer: Coding Test

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Angles, the Unit Circle and Trigonometric Graphs

Course outline (3 lessons)

Degrees, radians and the unit circle

Plotting sine, cosine and tangent

Checking identities in code

Test Your Learning

Your teacher

Discussion (0)