Simplify sec((5pi)/4)

Problem

sec((5*π)/4)

Solution

1. Identify the relationship between the secant function and the cosine function.

sec(θ)=1/cos(θ)

2. Determine the reference angle for (5*π)/4

(θ_ref)=(5*π)/4−π=π/4

3. Determine the quadrant of the angle.

π<(5*π)/4<(3*π)/2

(5*π)/4$i*s(i)*n*Q*u*a*d(r)*a*n*t*I*I*I,w*h*e*r*e*c*o*s(i)*n*e*a*n*d(s(e))*c*a*n*t*a*r*e*n*e*g*a*t*i*v*e.4.∗∗E*v*a*l*u*a*t*e∗∗t*h*e*c*o*s(i)*n*e*o*ƒ*t*h*e*a*n*g*l*e*u*s(i)*n*g*t*h*e*r*e*ƒ*e*r*e*n*c*e*a*n*g*l*e*a*n*d(q)*u*a*d(r)*a*n*t.$

\cos\left(\frac{5\pi}{4}\right) = -\cos\left(\frac{\pi}{4}\right)

\cos\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}

5.∗∗C*a*l*c*u*l*a*t*e∗∗t*h*e*s(e)*c*a*n*t*b*y*t*a*k*i*n*g*t*h*e*r*e*c*i*p*r*o*c*a*l*o*ƒ*t*h*e*c*o*s(i)*n*e*v*a*l*u*e.

\sec\left(\frac{5\pi}{4}\right) = \frac{1}{-\frac{\sqrt{2}}{2}}

\sec\left(\frac{5\pi}{4}\right) = -\frac{2}{\sqrt{2}}

6.∗∗R*a*t*i*o*n*a*l*i*z*e∗∗t*h*e*d(e)*n*o*m*i*n*a*t*o*r.

\sec\left(\frac{5\pi}{4}\right) = -\frac{2\sqrt{2}}{2}

\sec\left(\frac{5\pi}{4}\right) = -\sqrt{2}

$$ ## Final Answer $$

\sec\left(\frac{5\pi}{4}\right) = -\sqrt{2}

$$

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