Using Reference Angles to Find Trigonometric Function Values OBJECTIVE Find the value of any trigonometric function of a nonquadrantal angle θ. Step 1 Assuming that θ 360° or θ

Question

Using Reference Angles to Find Trigonometric Function Values

OBJECTIVE

Find the value of any trigonometric function of a nonquadrantal angle θ.

Step 1 Assuming that θ > 360° or θ < 0°, find a coterminal angle for θ with degree measure between 0° and 360°. Otherwise, go to Step 2.

Step 2 Find the reference angle θ′ for the angle resulting from Step 1.Write the trigonometric function of θ′.

Step 3 Choose the correct sign for the trigonometric function value of θ based on the quadrant in which it lies. Write the given trigonometric function of θ in terms of the same trigonometric function of θ′ with the appropriate sign.

Find sin 1320°.

Accepted Answer

Because [latex] 1320^{\circ}=3\left(360^{\circ} ight)+240^{\circ}, ext { the angle } 240^{\circ} [/latex] is coterminal with the angle 1320°.

Because 240° is in quadrant III, its reference angle θ' is

[latex] heta^{\prime}=240^{\circ}-180^{\circ}=60^{\circ} [/latex]

and

[latex] \sin heta^{\prime}=\sin 60^{\circ}=\frac{\sqrt{3}}{2} [/latex]

The angle 1320° and its coterminal angle, 240°, lie in quadrant III, where the sine is negative. So

[latex]\begin {matrix}\underset{\uparrow }{\sin 1320°} = \underset{\uparrow }{\sin 240°} & = \underset{\uparrow }{-\sin 60°} & = -\frac{\sqrt{3}}{2}. \ \fbox {coterminal angles } & \fbox {reference angle} & \end {matrix}[/latex]

Question 6.3.7: Using Reference Angles to Find Trigonometric Function Values...

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