Exam 7: Right Triangles and Vectors

Determine the $x$ and $y$ components of a vector of magnitude 631 that makes a 22.15 rad angle with the positive $x$ -axis.

A rectangle measures $55 \mathrm{~cm}$ by $39 \mathrm{~cm}$ . Find the angles between the diagonals to the nearest degree.

Vector A (magnitude 12) and vector $\mathbf{B}$ (magnitude 15) are perpendicular. Find the magnitude of the resultant and the angle it makes with $\mathbf{A}$ .

If $\mathbf{A}_{\mathbf{x}}=208$ and $\mathbf{A}_{\mathbf{y}}=378$ , find the magnitude of $\mathbf{A}$ and the angle $\theta$ it makes with the $x$ -axis.

Evaluate to four decimal places: $\cot 63^{\circ}-\sec 82^{\circ}$

Calculate the area of a parallelogram:

Evaluate sec $1.95^{\circ}$ to 2 decimal places.

If $\cos A=\frac{8}{37}$ , write the sin and tan of angle $A$ without using a calculator. Leave your answer in fractional form.

Express $\cos 16^{\circ}$ as a function of the complementary angle.

Blades on an in-water tidal turbine turn at 18 revolutions per minute. How fast is this in radians per second?

If $\mathbf{A}_{\mathbf{X}}=16.2$ and $\mathbf{A}_{\mathbf{y}}=4.1$ , find the magnitude of $\mathbf{A}$ and the angle $\theta$ it makes with the $x$ -axis.

The angle between the height and the slant height of a cone is $15.0^{\circ}$ . If the diameter of the circular base is $2.68 \mathrm{~cm}$ , what is the height of the cone?

A circuit has a resistance of $145 \Omega$ and an impedance of $325 \Omega$ . Find the reactance.

Express sec $78^{\circ}$ as a function of the complementary angle.

Express $\sin 47^{\circ} 58^{\prime}$ as a function of the complementary angle.

Evaluate $\csc 61.7^{\circ}$ to 3 significant digits.

Determine the $x$ and $y$ components of a vector of magnitude 415 that makes a $69.2^{\circ}$ angle with the positive $x$ -axis.

The point $(11,5)$ is on the terminal side of angle $\theta$ . Find the distance $r$ from the origin to the point and compute $\sin \theta, \cos \theta$ , and $\tan \theta$ . Work to 3 significant digits.

If $\sin \theta=0.416$ , what is $\theta$ in decimal degrees?

The arc length, $s$ , subtended by an angle $\theta$ in a circle of radius $r$ is given by $s=r \theta$ when the angle is measured in radians. What is the arc length subtended by a $55.3^{\circ}$ angle in a circle of radius $4.20 \mathrm{~cm}$ ?