Trigonometric functions and the unit circle | Matt Witchalls Maths Tuition

The other day, a student asked me:

“When I use the trig functions, what do the numbers on my calculator really mean?”

We discussed this question in detail and linked the output values from the SIN and COS calculator buttons for different angles to the horizontal and vertical measurements from the centre of the unit circle to a point P on the circumference. For example, when the angle $\theta$ is 0 degrees, the point P has coordinates (1, 0) and then when $\theta$ is 90 degrees, the coordinates are (0, 1).

By plotting the different values of the x and y coordinates for different points around the circumference of the circle, we were able to produce the graphs of the cosine and sine functions.

We also discussed the value of the tangent function as a ratio of the sine and cosine functions and why this leads to some of the more unsual features of the graph of tan ( $\theta$ ).

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