Math  /  Trigonometry

Question Find exact values for sec(θ)\sec (\theta), csc(θ)\csc (\theta), tan(θ)\tan (\theta), and cot(θ)\cot (\theta) when θ=5π4\theta=\frac{5 \pi}{4}.

Studdy Solution
Calculate cot(θ)\cot(\theta) as the reciprocal of tan(θ)\tan(\theta).
cot(5π4)=1tan(5π4)=11=1 \cot\left(\frac{5\pi}{4}\right) = \frac{1}{\tan\left(\frac{5\pi}{4}\right)} = \frac{1}{1} = 1
The exact values for the trigonometric functions at θ=5π4\theta = \frac{5\pi}{4} are: sec(θ)=2\sec(\theta) = -\sqrt{2} csc(θ)=2\csc(\theta) = -\sqrt{2} tan(θ)=1\tan(\theta) = 1 cot(θ)=1\cot(\theta) = 1

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