Pauline Y.

asked • 09/10/23

Use the figure to identify all angles between 0 and 2𝜋 satisfying the condition.

tan(𝜃)=−√3

Four points are marked on the circumference of each of the quadrants, and lines are drawn connecting these points with the center of the circle. First quadrant: First point at the intersection of the positive horizontal axis and the circumference of the circle is given as 0 (1, 0). Second point labeled pi over 6 has coordinates (squared root of 3 over 2, 1 over 2). Third point labeled pi over 4 has coordinates (squared root of 2 over 2, squared root of 2 over 2). Fourth point labeled pi over 3 has coordinates ( 1 over 2, squared root of 3 over 2). Second quadrant First point at the intersection of the positive vertical axis and the circumference of the circle is given as pi over 2. Second point - 2 times pi over 3, Third point - 3 times pi over 4, fourth point - five times pi over 6. Third quadrant First point at the intersection of the negative horizontal axis and the circumference of the circle is given as pi, second point - 7 times pi over 6, third point - 5 times pi over 4, fourth point - 4 times pi over 3. Fourth quadrant First point at the intersection of the negative vertical axis and the circumference of the circle is given as three times pi over 2, second point - five times pi over 3, third point 7 times pi over 4, fourth point - 11 times pi over 2.

(Give your answer in the form of a comma‑separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such 𝜃 exists on the interval [0,2𝜋].)



2 Answers By Expert Tutors

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Patrick F. answered • 09/11/23

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