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Chapter 4: Problem 56

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$-405^{\circ}$$

Short Answer

Expert verified
\(\cos(-405^{\circ}) = \sqrt{2}/2\), \(\sin(-405^{\circ}) = -\sqrt{2}/2\), \(\tan(-405^{\circ}) = -1\)

Step by step solution

01

Convert into Positive Angle

Add 360 degrees to the given angle until you obtain a positive angle. So we have, \(-405^{\circ} + 2 \times 360^{\circ} = 315^{\circ}\)
02

Value of Cosine, Sine and Tangent

Using the unit circle or known right triangle for \(315^{\circ}\), we have \(\cos(315^{\circ}) = \sqrt{2}/2\), \(\sin(315^{\circ}) = -\sqrt{2}/2\). Now, \(\tan(315^{\circ}) = \sin(315^{\circ}) \div \cos(315^{\circ}) = -1\)

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