Math  /  Trigonometry

QuestionFind (a) sinθ\sin \theta, (b) cosθ\cos \theta, and (c) tanθ\tan \theta for the given quadrantal angle. 11π11 \pi (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin(11π)=\sin (11 \pi)= \square (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The answer is undefined.

Studdy Solution
Now that we have the equivalent angle π\pi, we will find the trigonometric values using the unit circle.
(a) sinθ\sin \theta: The sine of π\pi is:
sin(π)=0 \sin(\pi) = 0
(b) cosθ\cos \theta: The cosine of π\pi is:
cos(π)=1 \cos(\pi) = -1
(c) tanθ\tan \theta: The tangent of π\pi is:
tan(π)=sin(π)cos(π)=01=0 \tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1} = 0
The values are: (a) sin(11π)=0\sin(11\pi) = 0 (b) cos(11π)=1\cos(11\pi) = -1 (c) tan(11π)=0\tan(11\pi) = 0

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