Chapter 14

In \(\triangle A B C, a=20 \mathrm{m}, b=14 \mathrm{m},\) and \(c=16 \mathrm{m} .\) Find \(m \angle A\)

Use a calculator and inverse functions to find the radian measures of the angles. angles whose tangent is \((-3)\)

Solve each trigonometric equation for \(0 \leq \theta < 2 \pi\) $$ \tan ^{2} \theta-\sec ^{2} \theta=\cos (-\theta) $$

Find each angle measure to the nearest tenth of a degree. \(\sin ^{-1} \frac{3}{4}\)

Simplify each trigonometric expression. $$ \sec ^{2} \theta-1 $$

Use a half-angle identity to find the exact value of each expression. $$ \tan 15^{\circ} $$

Use a calculator and inverse functions to find the radian measures of the angles. angles whose cosine is \((-0.89)\)

Solve each trigonometric equation for \(0 \leq \theta < 2 \pi\) $$ 2 \sin \left(\frac{\pi}{2}-\theta\right)=\sin (-\theta) $$

Find each angle measure to the nearest tenth of a degree. \(\tan ^{-1} \sqrt{3}\)

Simplify each trigonometric expression. $$ 1-\csc ^{2} \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \sin 15^{\circ} $$

In \(\triangle D E F, d=12 \mathrm{ft}, e=10 \mathrm{ft},\) and \(f=9 \mathrm{ft.}\) Find \(m \angle F\)

Solve each trigonometric equation for \(0 \leq \theta < 2 \pi\) $$ \tan \left(\frac{\pi}{2}-\theta\right)=\cos (-\theta) $$

Find each angle measure to the nearest tenth of a degree. \(\sin ^{-1} 0.335\)

In \(\triangle D E F, m \angle F=43^{\circ}, d=16 \mathrm{mm},\) and \(f=24 \mathrm{mm}\) . Find \(m \angle D\)

Simplify each trigonometric expression. $$ \sec \theta \cot \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \sin 22.5^{\circ} $$

Use a calculator and inverse functions to find the radian measures of the angles. angles whose tangent is 5

Find each angle measure to the nearest tenth of a degree. \(\cos ^{-1} 0.992\)

In \(\triangle A B C, m \angle A=52^{\circ}, c=10 \mathrm{ft},\) and \(a=15 \mathrm{ft} .\) Find \(m \angle C .\)

Simplify each trigonometric expression. $$ \cos \theta \tan \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \cos 22.5^{\circ} $$

In \(\triangle A B C, b=4\) in, \(c=6 \mathrm{in.},\) and \(m \angle A=69^{\circ} .\) Find \(m \angle C\)

Use a calculator and inverse functions to find the radian measures of the angles. angles whose cosine is 0.58

Use the definitions of the trigonometric ratios for a right triangle to derive each cofunction identity. a cofunction identity for \(\csc \left(90^{\circ}-A\right)\)

Find each angle measure to the nearest tenth of a degree. \(\tan ^{-1} 3.552\)

In \(\triangle X Y Z, m \angle Z=33^{\circ}, z=35 \mathrm{cm},\) and \(x=31 \mathrm{cm} .\) Find \(m \angle X .\)

Simplify each trigonometric expression. $$ \sin \theta \cot \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \tan 22.5^{\circ} $$

In \(\triangle R S T, r=17 \mathrm{cm}, s=12 \mathrm{cm},\) and \(m \angle T=13^{\circ} .\) Find \(m \angle S\)

Solve each equation for \(0 \leq \theta<2 \pi\). $$ 2 \sin \theta=1 $$

Use the definitions of the trigonometric ratios for a right triangle to derive each cofunction identity. a cofunction identity for \(\cot \left(90^{\circ}-A\right)\)

Find each angle measure to the nearest tenth of a degree. \(\sin ^{-1} 0.052\)

Simplify each trigonometric expression. $$ \sin \theta \csc \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \cos 90^{\circ} $$

\(\ln \triangle D E F, d=20 \mathrm{ft}, e=25 \mathrm{ft},\) and \(m \angle F=98^{\circ} .\) Find \(m \angle D\)

Solve each equation for \(0 \leq \theta<2 \pi\). $$ 2 \cos \theta-\sqrt{3}=0 $$

Mental Math Find the value of each trigonometric expression. $$ \cos 50^{\circ} \cos 40^{\circ}-\sin 50^{\circ} \sin 40^{\circ} $$

Find each angle measure to the nearest tenth of a degree. \(\cos ^{-1} \frac{3}{8}\)

Simplify each trigonometric expression. $$ \sec \theta \cos \theta \sin \theta $$

Use a half-angle identity to find the exact value of each expression. $$ \sin 7.5^{\circ} $$

Solve each equation for \(0 \leq \theta<2 \pi\). $$ 4 \tan \theta=3+\tan \theta $$

Mental Math Find the value of each trigonometric expression. $$ \sin 80^{\circ} \cos 35^{\circ}-\cos 80^{\circ} \sin 35^{\circ} $$

In \(\triangle A B C, \angle C\) is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. \(b=5, c=10\)

Simplify each trigonometric expression. $$ \sin \theta \sec \theta \cot \theta $$

Given \(\cos \theta=-\frac{4}{5}\) and \(90^{\circ}<\theta<180^{\circ},\) find the exact value of each expression. $$ \sin \frac{\theta}{2} $$

Solve each equation for \(0 \leq \theta<2 \pi\). $$ 2 \sin \theta-\sqrt{2}=0 $$

Mental Math Find the value of each trigonometric expression. $$ \sin 100^{\circ} \cos 170^{\circ}+\cos 100^{\circ} \sin 170^{\circ} $$

In \(\triangle A B C, \angle C\) is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. \(a=5, b=6\)

Simplify each trigonometric expression. $$ \sec ^{2} \theta-\tan ^{2} \theta $$