Find the exact radian value for 105^o.

Find the exact degree measure for \displaystyle \frac{13\pi}{24} .

Use a calculator to determine \displaystyle \sin \frac{15\pi}{17} .

Which of the these is an equivalent trigonometric expression for \sin x.

A. \displaystyle - \cos(\frac{\pi}{2} -x)

B. \displaystyle \sin(\frac{\pi}{2} -x)

C. \displaystyle \cos(\frac{\pi}{2} +x)

D. \displaystyle -\cos(\frac{\pi}{2} +x)

Find the exact value of \displaystyle \cos \frac{5\pi}{3} .

Given that \cot \theta = -1 and angle \theta lies in the second quadrant, what is \sec \thata?

Find \theta when \cos \theta = \displaystyle \cos \frac{\pi}{5}\cos \frac{\pi}{6} - \sin \frac{\pi}{5}\sin \frac{\pi}{6}

a) The Moon orbits Earth every 27.3 days. Determine the angular velocity of the Moon, in degrees per day and in radians per day.

b) The radius of the orbit of the Moon is about 384 400 km. How far does the Moon move along an arc of its orbit every day?

Determine an exact value for the expression

\displaystyle \frac{\sin \frac{\pi}{3} - \cos \frac{5\pi}{6}}{1 - \tan\frac{3\pi}{4}\cot \frac{\pi}{4}} .

An irregular building lot in a subdivision has the shape shown.

a) Determine an exact expression for the length of side x.

b) Determine an approximation for x, to the nearest tenth of a metre.

Give that \cos \frac{7\pi}{18} \approx 0.3420, determine the following, to four decimal places, without using a calculator. Justify your answers.

a) \displaystyle \sin \frac{\pi}{9}

b) \displaystyle \sin \frac{8\pi}{9}

Determine an exact value for \displaystyle \sin \frac{17\pi}{12} .

Angle x is in the second quadrant and angle y is in the first quadrant such that \sin x = \frac{7}{25} and \displaystyle \cos y = \frac{5}{13} .

a) Determine an exact value for \cos x.

b) Determine an exact value for \sin y.

c) Determine an exact value for \cos(x - y).

The manufacturer of a propeller for a small aircraft mandates a maximum operating angular velocity of 300 rad/s. Determine whether it is safe to install this propeller on an aircraft whose engine is expected to run at a maximum of 2800 rpm.

A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of \displaystyle \frac{\pi}{6} and sailed an additional 50 km.

Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise.

Prove that (\cos x - \sin x)^2 = 1 - \sin 2x.

Prove that \displaystyle 2\cos x \cos y = \cos(x + y) + \cos(x - y) .

Use a counterexample to show that \cos 2x + \sin 2y = 2\sin(x + y)cos(x - y) is not an identity.

Prove that \displaystyle (\csc x - \cot x)^2 = \frac{1 - \cos x}{1 + \cos x} .

A truss is used to hold up a heavy sign on a building, as shown. The truss is attached to the building along side AB, which measures 2.4 m. Determine an exact expression for the length CD.