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) $\mathrm { s } = \frac { 5 \pi } { 4 }$
B) $s = \frac { 4 \pi } { 3 }$
C) $s = \frac { 7 \pi } { 6 }$
D) $s = \frac { \pi } { 4 }$

Question

Quizplus · Accepted Answer

The tangent function equals 1 at an angle of $\frac{\pi}{4}$ radians. However, in the given interval $\left[ \pi , \frac { 3 \pi } { 2 } \right]$, the angle that also has a tangent of 1 is $\frac { 5 \pi } { 4 }$, because it is in the third quadrant where both sine and cosine are negative, making their ratio positive.

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 $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$