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)}

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!! 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