Question Video: Using the Unit Circle to Express the Values of Sine, Cosine, and Tangent for 2𝜋 − 𝑥 in Terms of Their Values for 𝑥, Where 𝑥 Is Any Real Number

In the figure, points 𝑀(cos 𝜃, sin 𝜃) and 𝑁 lie on the unit circle, and ∠𝐴𝑂𝑁 = 2𝜋 − 𝜃. Express the values of sine, cosine, and tangent of 2𝜋 − 𝜃 in terms of their values for 𝜃. Check whether this is valid for all values of 𝜃.

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