Trig function evaluation is a very important skill to acquire throughout math, especially when you don’t have a calculator. This is just one of the topics you must really master in order to further succeed in math.
Some things to memorize:
Conversions
Degrees to Radians:
x° \cdot\:\frac{\pi}{180}
Radians to Degrees:
x\pi \cdot\:\frac{180°}{\pi}
Even/Odd Identities
\sin(-\theta)=-\sin(\theta)
\csc(-\theta)=-\csc(\theta)
\cos(-\theta)=\cos(\theta)
\sec(-\theta)=\sec(\theta)
\tan(-\theta)=-\tan(\theta)
\cot(-\theta)=-\cot(\theta)
Reciprocal/Tangent Identities
\csc(\theta)=\frac{1}{\sin(\theta)}
\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}
\sec(\theta)=\frac{1}{\cos(\theta)}
\cot(\theta)=\frac{1}{\tan(\theta)}
Sum/Differences Identities
\sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta)
\cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta)
\tan(\alpha\pm\beta)=\frac{\tan(\alpha)\pm\tan(\beta)}{1\mp\tan(\alpha)\tan(\beta)}
!! This is your best friend. You really, really need to memorize the first quadrant. !!
I will now briefly talk about periodic functions. A periodic function is a function that repeats its value in regular periods. What does that mean? It means that for every period of π, π/2, 2π, etc., the function has the same value. Here are some periodic functions to memorize:
\mathrm{Let}\:n=0,\pm1,\pm2,\pm3,\ldots
\cos(\theta+2n\pi)=\cos(\theta)
\sin(\theta+2n\pi)=\sin(\theta)
\sec(\theta+2n\pi)=\sec(\theta)
\csc(\theta+2n\pi)=\csc(\theta)
\tan(\theta+n\pi)=\tan(\theta)
\cot(\theta+n\pi)=\cot(\theta)
There is no trick to evaluating trig functions. Memorizing what is above will help you to become successful in trig function evaluation.
Here’s an example (
click here):
Here’s another example (
click here):
Evaluating trig functions is pretty simple, but very important to know. For more practice, checkout Symbolab’s
practice.
Until next time,
Leah
