Question

Find the exact values of the six trigonometric functions of the angle 0 given in the figure. Use the Pythagorean Theorem to find the third side of the triangle.

Answer 1

since both sides are the same, you get the hypotenuse as
\[\sqrt{4^2+4^2}=\sqrt{2\times 16}=\sqrt{16}\times \sqrt{2}=4\sqrt{2}\] which tell you that to find the hypotenuse when both sides are equal, or to find the diagonal of a square multiply by \(\sqrt{2}\)

Answer 2

then use the trig ratios to find sine, cosine, tangent etc
tangent is easiest since \(\frac{opp}{adj}=\frac{4}{4}=1\) and therefore you know
\[\tan(45)=1\]

Answer 3

also \[\sin(45)=\frac{4}{4\sqrt{2}}=\frac{1}{\sqrt{2}}\] which you often seen written as \(\frac{\sqrt{2}}{2}\)

Answer 4

thank you :)

Answer 5

yw