Find the exact value of the expression.
-sec 3105°
A) $- \sqrt { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) 2
D) $\frac { 2 \sqrt { 3 } } { 3 }$

Question

Find the exact value of the expression.
-sec 3105° 
A) $- \sqrt { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) 2
D) $\frac { 2 \sqrt { 3 } } { 3 }$

Quizplus · Accepted Answer

Secant is the reciprocal of cosine. To find sec(3105°), first reduce the angle to one within the first cycle of 360°: 3105° - 8(360°) = 360° - 45° = 315°. Sec(315°) = 1/cos(315°). Cos(315°) = $\sqrt{2}/2$, so sec(315°) = 1/($\sqrt{2}/2$) = $\sqrt{2}$, but since 315° is in the fourth quadrant where sec is negative, the answer is $-\sqrt{2}$.

Find the Exact Value of the Expression −2- \sqrt { 2 }−2​

Find the Exact Value of the Expression $- \sqrt { 2 }$