Exam 15: Oblique Triangles and Vectors

Fill in the missing parts of this table for triangle $A B C$ .

State whether the following expressions are positive or negative, without using your calculator or your book. (a) $\cos 225^{\circ}$ (b) $\sin 314^{\circ}$ (c) $\cot 495^{\circ}$ (d) $\csc 820^{\circ}$ (e) $\tan \left(-220^{\circ}\right)$ (f) $\sec 195^{\circ}$

Write, to four significant digits, the sine, cosine, and tangent of $-105^{\circ}$ .

Find, to the nearest tenth of a degree, all angles less than $360^{\circ}$ whose trigonometric function is given. (a) $\sin \theta=-0.341$ (b) $\cos \theta=0.138$ (c) $\tan \theta=3.75$ (d) $\csc \theta=7 / 4$ (e) $\sec \theta=3 / 2$ (f) $\cot \theta=-3.75$

Solve the oblique triangle $A B C$ if $C=80.9^{\circ}, b=13.0$ , and $c=17.0$ .

Evaluate, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\theta=\sin^{-1} 0.59$ .

The resultant of two forces of $1500 \mathrm{~N}$ and $2500 \mathrm{~N}$ is $3200 \mathrm{~N}$ . What angle does the resultant force make with each of the forces?

In which quadrant will the terminal side of $\theta$ lie if $\theta=235^{\circ}$ ?

Find, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\tan \theta=2.018$ .

Write the sine, cosine and tangent of $\theta$ , where $\sin \theta=5 / 13$ and $\tan \theta$ is positive. Leave your answers in fractional or radical form.

Solve the oblique triangle $A B C$ if $a=7.52, b=8.40$ , and $c=12.1$ . Round answers to the nearest whole number.

Fill in the missing parts of this table for triangle $A B C$ .

Two vectors of magnitude $A=16.6$ and $B=19.0$ are separated by an angle $\theta=61.0^{\circ}$ . Find the resultant and the angle the resultant makes with vector $B$ .

Solve the oblique triangle $A B C$ if $A=53.3^{\circ}, C=29.4^{\circ}$ , and $c=12.8$ .

What force must the weight in the figure below exert to keep the system in equilibrium?

Give the algebraic signs of the sine, cosine, and tangent of $176^{\circ}$ .

State whether the following expressions are positive or negative, without using your calculator or your book. (a) $\cos 135^{\circ}$ (b) $\sin 179^{\circ}$ (c) $\cot 147^{\circ}$ (d) $\csc \left(-700^{\circ}\right)$ (e) $\tan \left(439^{\circ}\right)$ (f) $\sec \left(-149^{\circ}\right)$

Write the sine, cosine, and tangent of the angle $\theta$ whose terminal side passes through the point $(6,-5)$ . Use three significant digits in your answers.

Point $A$ is $45.0 \mathrm{~m}$ from point $B$ and $64.5 \mathrm{~m}$ from point $C$ . An observer at $A$ measures angle $B A C$ to be $34.0^{\circ}$ . How far apart are $B$ and $C$ ?

Fill in the missing parts of this table for triangle $A B C$ .