Section 1
Trigonometric Functions of Acute Angles
Find the six trigonometric function values of the specified angle.(Graph can't copy)
Given that $\sin \alpha=\frac{\sqrt{5}}{3}, \cos \alpha=\frac{2}{3},$ and$\tan \alpha=\frac{\sqrt{5}}{2},$ find $\csc \alpha, \sec \alpha,$ and $\cot \alpha$
Given that $\sin \beta=\frac{2 \sqrt{2}}{3}, \cos \beta=\frac{1}{3},$ and$\tan \beta=2 \sqrt{2},$ find $\csc \beta, \sec \beta,$ and $\cot \beta$
Given a function value of an acute angle, find the other five trigonometric function values.$$\sin \theta=\frac{24}{25}$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\cos \sigma=0.7$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\tan \phi=2$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\cot \theta=\frac{1}{3}$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\csc \theta=1.5$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\sec \beta=\sqrt{17}$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\cos \beta=\frac{\sqrt{5}}{5}$$
Given a function value of an acute angle, find the other five trigonometric function values.$$\sin \sigma=\frac{10}{11}$$
Find the exact function value.$$\cos 45^{\circ}$$
Find the exact function value.$$\tan 30^{\circ}$$
Find the exact function value.$$\sec 60^{\circ}$$
Find the exact function value.$$\sin 45^{\circ}$$
Find the exact function value.$$\cot 60^{\circ}$$
Find the exact function value.$$\csc 45^{\circ}$$
Find the exact function value.$$\sin 30^{\circ}$$
Find the exact function value.$$\cos 60^{\circ}$$
Find the exact function value.$$\tan 45^{\circ}$$
Find the exact function value.$$\sec 30^{\circ}$$
Find the exact function value.$$\csc 30^{\circ}$$
Find the exact function value.$$\tan 60^{\circ}$$
Four Square. The game Four Square is making a comeback on college campuses. The game is played on a 16 -ft square court divided into four smaller squares that meet in the center. If a line is drawn diagonally from one corner to another corner, then a right triangle $Q T S$ is formed, where $\angle Q T S$ is $45^{\circ} .$ Using a trigonometric function, find the length of the diagonal. Round the answer to the nearest tenth of a foot.
Height of a Hot-Air Balloon. As a hot-air balloon began to rise, the ground crew drove $1.2 \mathrm{mi}$ to an observation station. The initial observation from the station estimated the angle between the ground and the line of sight to the balloon to be $30^{\circ} .$ Approximately how high was the balloon at that point? (We are assuming that the wind velocity was low and that the balloon rose vertically for the first few minutes.)
Convert to decimal degree notation. Round to two decimal places.$$9^{\circ} 43^{\prime}$$
Convert to decimal degree notation. Round to two decimal places.$$52^{\circ} 15^{\prime}$$
Convert to decimal degree notation. Round to two decimal places.$$35^{\circ} 50^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$64^{\circ} 53^{\prime}$$
Convert to decimal degree notation. Round to two decimal places.$$3^{\circ} 2^{\prime}$$
Convert to decimal degree notation. Round to two decimal places.$$19^{\circ} 47^{\prime} 23^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$49^{\circ} 38^{\prime} 46^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$76^{\circ} 11^{\prime} 34^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$15^{\prime} 5^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$68^{\circ} 2^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$5^{\circ} 53^{\prime \prime}$$
Convert to decimal degree notation. Round to two decimal places.$$44^{\prime} 10^{\prime \prime}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$17.6^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$20.14^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$83.025^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$67.84^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$11.75^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$29.8^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$47.8268^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$0.253^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$0.9^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$30.2505^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$39.45^{\circ}$$
Convert to degrees, minutes, and seconds. Round to the nearest second.$$2.4^{\circ}$$
Find the function value. Round to four decimal places.$$\cos 51^{\circ}$$
Find the function value. Round to four decimal places.$$\cot 17^{\circ}$$
Find the function value. Round to four decimal places.$$\tan 4^{\circ} 13^{\prime}$$
Find the function value. Round to four decimal places.$$\sin 26.1^{\circ}$$
Find the function value. Round to four decimal places.$$\sec 38.43^{\circ}$$
Find the function value. Round to four decimal places.$$\cos 74^{\circ} 10^{\prime} 40^{\prime \prime}$$
Find the function value. Round to four decimal places.$$\cos 40.35^{\circ}$$
Find the function value. Round to four decimal places.$$\csc 45.2^{\circ}$$
Find the function value. Round to four decimal places.$$\sin 69^{\circ}$$
Find the function value. Round to four decimal places.$$\tan 63^{\circ} 48^{\prime}$$
Find the function value. Round to four decimal places.$$\tan 85.4^{\circ}$$
Find the function value. Round to four decimal places.$$\cos 4^{\circ}$$
Find the function value. Round to four decimal places.$$\csc 89.5^{\circ}$$
Find the function value. Round to four decimal places.$$\sec 35.28^{\circ}$$
Find the function value. Round to four decimal places.$$\cot 30^{\circ} 25^{\prime} 6^{\prime \prime}$$
Find the function value. Round to four decimal places.$$\sin 59.2^{\circ}$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\sin \theta=0.5125$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\tan \theta=2.032$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\tan \theta=0.2226$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\cos \theta=0.3842$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\sin \theta=0.9022$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\tan \theta=3.056$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\cos \theta=0.6879$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\sin \theta=0.4005$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\cot \theta=2.127$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\csc \theta=1.147$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\sec \theta=1.279$$
Find the acute angle $\theta,$ to the nearest tenth of a degree, for the given function value.$$\cot \theta=1.351$$
Find the exact acute angle for the given function value.$$\sin \theta=\frac{\sqrt{2}}{2}$$
Find the exact acute angle for the given function value.$$\cot \theta=\frac{\sqrt{3}}{3}$$
Find the exact acute angle for the given function value.$$\cos \theta=\frac{1}{2}$$
Find the exact acute angle for the given function value.$$\sin \theta=\frac{1}{2}$$
Find the exact acute angle for the given function value.$$\tan \theta=1$$
Find the exact acute angle for the given function value.$$\cos \theta=\frac{\sqrt{3}}{2}$$
Find the exact acute angle for the given function value.$$\csc \theta=\frac{2 \sqrt{3}}{3}$$
Find the exact acute angle for the given function value.$$\tan \theta=\sqrt{3}$$
Find the exact acute angle for the given function value.$$\cot \theta=\sqrt{3}$$
Find the exact acute angle for the given function value.$$\sec \theta=\sqrt{2}$$
Use the cofunction and reciprocal identities to complete each of the following.$$\cos 20^{\circ}=\text{_____}70^{\circ}=\frac{1}{\text{____}20^{\circ}}$$
Use the cofunction and reciprocal identities to complete each of the following.$$\sin 64^{\circ}=\text{____} 26^{\circ}=\frac{1}{\text{____}64^{\circ}}$$
Use the cofunction and reciprocal identities to complete each of the following.$$\tan 52^{\circ}=\cot\text {____}={\frac{1}{\text{____}52^{\circ}}}$$
Use the cofunction and reciprocal identities to complete each of the following.$$\sec 13^{\circ}=\csc\text{____}={\frac{1}{\text{____}13^\circ}}$$
Given that$$\begin{aligned}&\sin 65^{\circ} \approx 0.9063, \quad \cos 65^{\circ} \approx 0.4226\\&\tan 65^{\circ} \approx 2.1445, \quad \cot 65^{\circ} \approx 0.4663\\&\sec 65^{\circ} \approx 2.3662, \quad \csc 65^{\circ} \approx 1.1034\end{aligned}$$find the six function values of $25^{\circ} .$
Given that$$\begin{array}{ll}\sin 8^{\circ} \approx 0.1392, & \cos 8^{\circ} \approx 0.9903 \\\tan 8^{\circ} \approx 0.1405, & \cot 8^{\circ} \approx 7.1154 \\\sec 8^{\circ} \approx 1.0098, & \csc 8^{\circ} \approx 7.1853\end{array}$$find the six function values of $82^{\circ} .$
Given that $\sin 71^{\circ} 10^{\prime} 5^{\prime \prime} \approx 0.9465$$\cos 71^{\circ} 10^{\prime} 5^{\prime \prime} \approx 0.3228,$ and$\tan 71^{\circ} 10^{\prime} 5^{\prime \prime} \approx 2.9321$find the six function values of $18^{\circ} 49^{\prime} 55^{\prime \prime}$
Given that $\sin 38.7^{\circ} \approx 0.6252$$\cos 38.7^{\circ} \approx 0.7804,$ and $\tan 38.7^{\circ} \approx 0.8012$find the six function values of $51.3^{\circ} .$
Given that $\sin 82^{\circ}=p, \cos 82^{\circ}=q,$ and$\tan 82^{\circ}=r,$ find the six function values of $8^{\circ}$ in terms of $p, q,$ and $r$
Graph the function.$$f(x)=2^{-x}$$
Graph the function.$$f(x)=e^{x / 2}$$
Graph the function.$$g(x)=\log _{2} x$$
Graph the function.$$h(x)=\ln x$$
Solve.$$e^{t}=10,000$$
Solve.$$5^{x}=625$$
Solve.$$\log (3 x+1)-\log (x-1)=2$$
Solve.$$\log _{7} x=3$$
Given that $\cos \theta=0.9651,$ find $\csc \left(90^{\circ}-\theta\right)$
Given that $\sec \beta=1.5304,$ find $\sin \left(90^{\circ}-\beta\right)$
Find the six trigonometric function values of $\alpha .$(Angle can't copy)
Show that the area of this right triangle is$$\frac{1}{2} b c \sin A$$(Angle can't copy)
Show that the area of this triangle is$$\frac{1}{2} a b \sin \theta$$(Angle can't copy)