Trigonometry

Trigonometry, a significant branch of mathematics, examines the connections between the lengths of sides and angles in triangles. It brings forward important concepts such as sine, cosine, and tangent which are integral to fields like physics, engineering, and computer science. Trigonometric functions play a crucial role in comprehending cycles, waves, and phenomena that occur periodically.

Converting Radians to Degrees

Convert \(\frac{5\pi}{6}\) radians to degrees.

Converting Degrees to Radians

Convert 120 degrees to radians.

Right Triangle Trigonometry

In a right triangle, one of the angles is 30 degrees and the length of the hypotenuse is 10 units. What is the length of the side opposite to the 30 degree angle?

Graphing Sine & Cosine Functions

Graph the function \(y = 2\sin(x - \frac{\pi}{3})\).

Amplitude, Period, and Phase Shift

A population of mice is at its lowest in January $(t=0)$ and oscillates 18 above and below an average of 107 during the year. Find an equation for the population, $P$, in terms of the months since January, $t$.

Finding a Reference Angle

Find the reference angle for \(230^\circ\).

Finding a Supplement

Find the supplement of an angle whose measure is \(45^\circ\).

Finding a Complement

If \(\sin{\theta} = 0.6\), find the complement angle \(\theta'\) in degrees.

Finding the Quadrant of the Angle

In which quadrant is the angle \( \theta = 5 \pi / 4 \) located?