Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$$
A) $s = \frac { \pi } { 4 }$

B) $s = \frac { 4 \pi } { 3 }$

C) $s = \frac { 7 \pi } { 6 }$

D) $s = \frac { 5 \pi } { 4 }$

Question

Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$$
A) $s = \frac { \pi } { 4 }$

B) $s = \frac { 4 \pi } { 3 }$

C) $s = \frac { 7 \pi } { 6 }$

D) $s = \frac { 5 \pi } { 4 }$

Quizplus · Accepted Answer

The tangent function, $\tan(s) = 1$, has a solution at $s = \frac{\pi}{4}$ in the first quadrant. However, since we are looking for the solution in the interval $\left[ \pi , \frac { 3 \pi } { 2 } \right]$, which is in the third quadrant, we need to find the equivalent angle in this quadrant. The equivalent angle in the third quadrant where $\tan(s) = 1$ is $s = \frac{5\pi}{4}$, as the tangent function is positive in both the first and third quadrants.

Find the Exact Value of S in the Given Interval [π,3π2];tan⁡s=1\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1[π,23π​];tans=1

Find the Exact Value of S in the Given Interval $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$