Question

What are the values of each of the 6 different trigonometric functions? Drag the correct value into each box.

Answer 1

All of those values are reflections of well know values of those functions. We are familiar with the sine, cosine and tangent of 30º, 45º, 60º and 90º.

With this previous knowledge(you might look for a table with those values) we can answer those questions.

The first one is direct

`\sin 60^o=\frac{\sqrt[]{3}}{2}`

-300º is the same as 60º, since a full circle is 360º and with the minus sign it means it was rotating in the other direction, then

`\sin (-300^o)=\frac{\sqrt[]{3}}{2}`

Converting from radians

`\begin{gathered} (\pi)/(2)=90^o \\ (5\pi)/(2)=(\pi)/(2)+2\pi=450^o \end{gathered}`

Then

`\cos (\pi)/(2)=0`

And 450º, is a full circle with an addition of 90º. After a full circle the trigonometric functions repeat their value. Then

`\cos (5\pi)/(2)=\cos (\pi)/(2)=0`

Again, we have a similar situation. -45º and 315º are the same angle, just rotations in different directions. The tangent of -45º is just the negative of the tangent of 45º. then

`\tan (315^o)=\tan (-45^o)=-\tan (45^o)=-1`