Math  /  Trigonometry

QuestionThe point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle. (312,215)sinθ=cosθ=tanθ=cscθ=secθ=cotθ=\begin{array}{l} \left(3 \frac{1}{2},-2 \sqrt{15}\right) \\ \sin \theta=\square \\ \cos \theta=\square \\ \tan \theta=\square \\ \csc \theta=\square \\ \sec \theta=\square \\ \cot \theta=\square \end{array}

Studdy Solution
Calculate the cotangent function cotθ \cot \theta :
cotθ=1tanθ=14157=7415=74151515=71560 \cot \theta = \frac{1}{\tan \theta} = \frac{1}{\frac{-4 \sqrt{15}}{7}} = \frac{7}{-4 \sqrt{15}} = -\frac{7}{4 \sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}} = -\frac{7 \sqrt{15}}{60}
Solution: sinθ=41517 \sin \theta = -\frac{4 \sqrt{15}}{17} cosθ=717 \cos \theta = \frac{7}{17} tanθ=4157 \tan \theta = -\frac{4 \sqrt{15}}{7} cscθ=171560 \csc \theta = -\frac{17 \sqrt{15}}{60} secθ=177 \sec \theta = \frac{17}{7} cotθ=71560 \cot \theta = -\frac{7 \sqrt{15}}{60}

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