Chapter 10

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \sin (5 x)=0 $$

Find the exact value. \(\arcsin (-1)\)

In Exercises \(1-12,\) graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=3 \sin (x)\)

In Exercises \(1-6,\) use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \sin (3 \pi-2 \theta)=-\sin (2 \theta-3 \pi) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \tan \left(\frac{\pi}{4}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=0 $$

Convert the angles into the DMS system. Round each of your answers to the nearest second. $$ 63.75^{\circ} $$

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \cos (3 x)=\frac{1}{2} $$

Find the exact value. \(\arcsin \left(-\frac{\sqrt{3}}{2}\right)\)

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=\sin (3 x)\)

Use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \cos \left(-\frac{\pi}{4}-5 t\right)=\cos \left(5 t+\frac{\pi}{4}\right) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \sec \left(\frac{\pi}{6}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\frac{\pi}{4} $$

Convert the angles into the DMS system. Round each of your answers to the nearest second. $$ 200.325^{\circ} $$

Find the exact value. \(\arcsin \left(-\frac{\sqrt{2}}{2}\right)\)

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \sin (-2 x)=\frac{\sqrt{3}}{2} $$

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=-2 \cos (x)\)

Use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \tan \left(-t^{2}+1\right)=-\tan \left(t^{2}-1\right) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \csc \left(\frac{5 \pi}{6}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\frac{\pi}{3} $$

Convert the angles into the DMS system. Round each of your answers to the nearest second. $$ -317.06^{\circ} $$

Find the exact value. \(\arcsin \left(-\frac{1}{2}\right)\)

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \tan (6 x)=1 $$

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=\cos \left(x-\frac{\pi}{2}\right)\)

Use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \csc (-\theta-5)=-\csc (\theta+5) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \cot \left(\frac{4 \pi}{3}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\frac{\pi}{2} $$

Convert the angles into the DMS system. Round each of your answers to the nearest second. $$ 179.999^{\circ} $$

Find the exact value. \(\arcsin (0)\)

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\).] $$ \csc (4 x)=-1 $$

Use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \sec (-6 t)=\sec (6 t) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \tan \left(-\frac{11 \pi}{6}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\frac{2 \pi}{3} $$

Convert the angles into decimal degrees. Round each of your answers to three decimal places. $$ 125^{\circ} 50^{\prime} $$

Find the exact value. \(\arcsin \left(\frac{1}{2}\right)\)

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \sec (3 x)=\sqrt{2} $$

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=\sin (2 x-\pi)\)

Use the Even / Odd Identities to verify the identity. Assume all quantities are defined. $$ \cot (9-7 \theta)=-\cot (7 \theta-9) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \sec \left(-\frac{3 \pi}{2}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\frac{3 \pi}{4} $$

In Exercises \(69-80,\) solve the inequality. Express the exact answer in interval notation, restricting your attention to \(0 \leq x \leq 2 \pi\). $$ \sec ^{2}(x) \leq 4 $$

Find the exact value. \(\arcsin \left(\frac{\sqrt{2}}{2}\right)\)

In Exercises \(1-18,\) find all of the exact solutions of the equation and then list those solutions which are in the interval \([0,2 \pi)\). $$ \cot (2 x)=-\frac{\sqrt{3}}{3} $$

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=-\frac{1}{3} \cos \left(\frac{1}{2} x+\frac{\pi}{3}\right)\)

In Exercises 7 - 21 , use the Sum and Difference Identities to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. $$ \cos \left(75^{\circ}\right) $$

In Exercises 1 - 20 , find the exact value or state that it is undefined. $$ \csc \left(-\frac{\pi}{3}\right) $$

Find the exact value of the cosine and sine of the given angle. $$ \theta=\pi $$

Find the exact value. \(\arcsin \left(\frac{\sqrt{3}}{2}\right)\)

Graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. \(y=\cos (3 x-2 \pi)+4\)

Use the Sum and Difference Identities to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. $$ \sec \left(165^{\circ}\right) $$