December 6, 2024
Introduction The answer to this question is \[\begin{align*} \boxed{\cos \dfrac{\pi}{4} = \dfrac{\sqrt{2}}{2}} \end{align*}\] In this article, we’ll learn how to find \(\cos \dfrac{\pi}{4}\), which is the same as \(\cos 45^\circ\). We’ll approach this by using both a right triangle and the unit circle. After that, we’ll go through a practical example where knowing \(\cos \dfrac{\pi}{4}\) […]
November 15, 2024
Introduction to Radian and Degree Conversion Trigonometry often uses radians as a way to measure angles, although degrees are also common in many applications. Knowing how to convert between these units is essential. The main relationship between radians and degrees is: \[\begin{align*} \pi \text{ radians} = 180^\circ \end{align*}\] If we divide both sides by 3 […]
November 15, 2024
Cosine of $\pi$ is $\boxed{-1}$. 1 Unit Circle There are multiple ways to find $\cos \pi$. One option is to use the unit circle: Notice that $\cos \pi = \cos 180^\circ$. Recall that $180^\circ$ is a straight angle, so the terminal side in standard position would intersect the unit circle on the $x$-axis at $(-1,0)$. […]
November 15, 2024
Unit Circle The unit circle is defined by $x^2 + y^2 = 1$, which is a circle with radius $1$, centered at the origin $(0, 0)$. An example of the unit circle is below: Standard Position of an Angle An angle is in standard position if its initial side is on the positive $x$-axis, its […]
November 15, 2024
The unit circle is defined as $x^2 + y^2 = 1$, which is a circle with radius $1$, centered at the origin $(0, 0)$. It is used in trigonometry to simplify finding values of trig functions. An empty unit circle is below with markings to be filled in: Blank_Unit_Circle.PDF Practice Problems Find the radian value […]
October 11, 2024
The value of \(\cos 180^\circ\) is: $\cos 180^\circ = \boxed{-1}$ Explanation To understand why, let’s look at the unit circle. The cosine of an angle corresponds to the \(x\)-coordinate of the point on the unit circle at that angle. We measure angles by moving counterclockwise from the positive \(x\)-axis. Thus at \(180^\circ\), we’re at the […]
