8.2 Trigonometric Functions of Any Angle

  • Reference Angle • Evaluating Trigonometric Functions • Evaluations on a Calculator • Quadrantal Angles • Negative Angles

In the last section, we saw that the signs of the trigonometric functions depend on the quadrant of θ .  In this section, we will investigate an important connection between certain angles in different quadrants. To illustrate this, let’s start by taking the sine of the angles 20 ° , 160 ° , 200 ° , and 340 ° . These values are shown in Fig. 8.5.

A calculator screen with inputs for sine of 20, sine of 160, sine of 200, and sine of 340. Outputs for the first two inputs are each 0.3420201433, and outputs for the last two are each negative 0.3420201433.

Fig. 8.5

The signs of the function values agree with what we would expect; sin θ is positive in quadrants I and II and negative in quadrants ...

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