Chapter 8

Solve triangle \(A B C\). $$A=25.2^{\circ} \quad a=7.14 \quad c=13.2$$

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if $$\theta=845^{\circ}.$$

Two forces of \(18.6 \mathrm{N}\) and \(21.7 \mathrm{N}\) are applied to a point on a body. The angle between the forces is \(44.6^{\circ} .\) Find the magnitude of the resultant and the angle that it makes with the larger force.

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if \(\sin \theta\) is positive.

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$486^{\circ}$$

Two forces whose magnitudes are 187 lb and 206 lb act on an object. The angle between the forces is \(88.4^{\circ} .\) Find the magnitude of the resultant force.

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if \(\cos \theta\) is negative.

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$-527^{\circ}$$

Writing: What happens to the law of sines when the angle for which it is written is a right angle? Explain in a paragraph.

If \(\theta\) is an angle in standard position, state in what quadrants its terminal side can lie if \(\sec \theta\) is positive.

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$114^{\circ} 23^{\prime}$$

Forces of 675 lb and 828 lb act on a body. The smaller force acts due north: the larger force acts \(\mathrm{N} 52.3^{\circ} \mathrm{E}\). Find the direction and the magnitude of the resultant.

A pole standing on level ground makes an angle of \(85.8^{\circ}\) with the horizontal. The pole is supported by a 22.0 -ft prop whose base is \(12.5 \mathrm{ft}\) from the base of the pole. Find the angle made by the prop with the horizontal.

State whether the following expressions are positive or negative. Do not use your calculator, and try not to refer to your book. $$\sin 174^{\circ}$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$-11^{\circ} 18^{\prime}$$

Two forces of \(925 \mathrm{N}\) and \(1130 \mathrm{N}\) act on an object. Their lines of action make an angle of \(67.2^{\circ}\) with each other. Find the magnitude and the direction of their resultant.

State whether the following expressions are positive or negative. Do not use your calculator, and try not to refer to your book. $$\cos 110^{\circ}$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$412^{\circ}$$

State whether the following expressions are positive or negative. Do not use your calculator, and try not to refer to your book. $$\tan 315^{\circ}$$

Trigonometric Functions of Any Angle by Calculator. Write, to four significant digits, the sine, cosine, and tangent of each angle. $$238^{\circ}$$

State whether the following expressions are positive or negative. Do not use your calculator, and try not to refer to your book. $$\sec 332^{\circ}$$

Reciprocal Relationships. Evaluate to four decimal places. Find \(\csc \theta\) if \(\sin \theta=0.7352\)

Reciprocal Relationships. Evaluate to four decimal places. Find \(\sec \theta\) if \(\cos \theta=0.7354\)

Give the algebraic signs of the sine, cosine, and tangent of the following. Do not use your calculator. $$110^{\circ}$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\sec 158.3^{\circ}$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\cot 153.6^{\circ}$$

Find the lengths of the diagonals of a parallelogram, two of whose sides are \(3.75 \mathrm{m}\) and \(1.26 \mathrm{m} ;\) their included angle is \(68.4^{\circ}\)

Give the algebraic signs of the sine, cosine, and tangent of the following. Do not use your calculator. $$335^{\circ}$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\csc 122.7^{\circ}$$

A plane flies with a heading of \(\mathrm{N} 48.0^{\circ} \mathrm{W}\) and an air speed of \(584 \mathrm{km} / \mathrm{h}\). It is driven from its course by a wind of \(58.0 \mathrm{km} / \mathrm{h}\) from \(\mathrm{S} 12.0^{\circ} \mathrm{E} .\) Find the ground speed and the drift angle of the plane.

Give the algebraic signs of the sine, cosine, and tangent of the following. Do not use your calculator. $$-48^{\circ}$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\csc 207.4^{\circ}$$

The sides of a triangle are \(124,175,\) and \(208 .\) Find the length of the median drawn to the longest side.

Give the algebraic signs of the sine, cosine, and tangent of the following. Do not use your calculator. $$500^{\circ}$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\sec 215.4^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\sin \theta=0.7761$$

Cotangent, Secant, and Cosecant by Calculator. Evaluate to four decimal places. $$\cot 228.7^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\tan \theta=-0.1587$$

The sides of a triangle are in the ratio \(2: 3: 4 .\) Find the cosine of the largest angle.

Cofunctions. Express as a function of the complementary angle. $$\sin 38^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\cos \theta=0.8372$$

Cofunctions. Express as a function of the complementary angle. $$\cos 73^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\cos \theta=0.3215$$

Cofunctions. Express as a function of the complementary angle. $$\tan 19^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\tan \theta=6.372$$

Cofunctions. Express as a function of the complementary angle. $$\sec 85.6^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\cos \theta=0.4476$$

Cofunctions. Express as a function of the complementary angle. $$\cot 63.2^{\circ}$$

Cofunctions. Express as a function of the complementary angle. $$\csc 82.7^{\circ}$$

Find two positive angles less than \(360^{\circ}\) whose trigonometric function is given. Round your angles to a tenth of a degree. $$\cot \theta=2.8458$$