Math  /  Trigonometry

QuestionFind the values of the six trigonometric functions for the angle π4\frac{\pi}{4} without using a calculator.

Studdy Solution
The cotangent of an angle is defined as the reciprocal of the tangent of the angle.
cot(π4)=1tan(π4)=11=1\cot(\frac{\pi}{4}) = \frac{1}{\tan(\frac{\pi}{4})} = \frac{1}{1} =1So, the exact values of the six trigonometric functions for the angle π4\frac{\pi}{4} aresin(π4)=22\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}cos(π4)=22\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}tan(π4)=1\tan(\frac{\pi}{4}) =1csc(π4)=2\csc(\frac{\pi}{4}) = \sqrt{2}sec(π4)=2\sec(\frac{\pi}{4}) = \sqrt{2}cot(π4)=1\cot(\frac{\pi}{4}) =1

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