Answer:
Considering the sign behavior of each function and the angle and its multiples.
Step-by-step explanation:
1) Firstly, look at the Unit Circle below. In the Unit Circle we can with the aid of symmetry, find angles with the same height, and also the same angle value.
2) We need to remember or get to know the behavior of the trigonometric functions, in order to know whether it is positive or negative. Let's work with the tree basic ones: sine, cosine and tangent.
3) Let's take the 60º angle, to exemplify.
Symmetric angles have the same height proportional values for their angles.
Notice that the angle of 60º ∈ Quadrant II, and 120º ∈ Quadrant II and 240º for Quadrant III and 300º for Quadrant IV as well.
We can calculate their values, considering their sign behavior each quadrant for cosine function.
Similarly, for the sine function, don't forget to consider sign behavior for each quadrant
[tex]cos60^{\circ}=\frac{1}{2}\\cos 120^{\circ}= -cos60^{\circ}=-\frac{1}{2}\\cos 240 ^{\circ}=-cos60^{\circ}=-\frac{1}{2}\\cos 300^{\circ}= cos60^{\circ}=\frac{1}{2}[/tex]
Similarly, for sine function, don't forget to considering sign behavior for each quadrant
[tex]sin 60^{\circ}=\frac{\sqrt{3}}{2} \\sin 120^{\circ}=sin 60^{\circ}=\frac{\sqrt{3}}{2} \\\\sin 240^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2} \\\\sin 300^{\circ} =-sin 60^{\circ}=\frac{-\sqrt{3}}{2}[/tex]
And finally, for the tangent function
[tex]tan 60^{\circ}=\sqrt{3} \\tan 120^{\circ}=-tan 60^{\circ}=-\sqrt{3}\\tan 240^{\circ}=tan 60^{\circ}=\sqrt{3}\\tan 300^{\circ}=-tan 60^{\circ}=-\sqrt{3}[/tex]
