Without using a calculator, give the exact trigonometric function value with rational denominator.
-sec 45
A) $\sqrt { 2 }$
B) 1
C) $\frac { 1 } { 2 }$
D) $\frac { 2 \sqrt { 3 } } { 3 }$ °

Question

Without using a calculator, give the exact trigonometric function value with rational denominator.
-sec 45 
A) $\sqrt { 2 }$
B) 1
C) $\frac { 1 } { 2 }$
D) $\frac { 2 \sqrt { 3 } } { 3 }$ °

Quizplus · Accepted Answer

The secant of 45 degrees is equal to the reciprocal of the cosine of 45 degrees. Since $\cos(45^\circ) = \frac{\sqrt{2}}{2}$, the secant, which is the reciprocal, is $\sec(45^\circ) = \frac{1}{\cos(45^\circ)} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}$.

Without Using a Calculator, Give the Exact Trigonometric Function Value 2\sqrt { 2 }2​

Without Using a Calculator, Give the Exact Trigonometric Function Value $\sqrt { 2 }$