Math  /  Trigonometry

QuestionQuestion 14 (1 point) Determine the exact value of tan7π6\tan \frac{7 \pi}{6}. a) 13-\frac{1}{\sqrt{3}} b) 13\frac{1}{\sqrt{3}} C) 32-\frac{\sqrt{3}}{2} d) 32\frac{\sqrt{3}}{2}

Studdy Solution
Use the reference angle and quadrant to find the exact value of tan7π6\tan \frac{7\pi}{6}:
In the third quadrant, the tangent function is positive. The tangent of the reference angle π6\frac{\pi}{6} is:
tanπ6=13 \tan \frac{\pi}{6} = \frac{1}{\sqrt{3}}
Since tan\tan is positive in the third quadrant:
tan7π6=13 \tan \frac{7\pi}{6} = \frac{1}{\sqrt{3}}
The exact value of tan7π6\tan \frac{7\pi}{6} is:
13 \boxed{\frac{1}{\sqrt{3}}}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord