Question

Express the trig ratios as fractions in simplest terms.J1617IV33Ksin J =cos K =are equalare not equalsin J and cos K

Answer 1

The three basic trigonometric ratios for a specific angle θ are sine, cosine, and tangent:

$\begin{gathered} \sin (\theta)=\frac{\text{ Opposite side}}{\text{ Hypotenuse}} \\ \cos (\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \tan (\theta)=\frac{\text{Opposite side}}{\text{Adjacent side}} \end{gathered}$

So, in this case, we have:

First ratio

$\begin{gathered} \theta=J \\ \text{ Opposite side }=\sqrt[]{33} \\ \text{ Hypotenuse }=17 \\ \sin (\theta)=\frac{\text{ Opposite side}}{\text{ Hypotenuse}} \\ \boldsymbol{\sin (J)=\frac{\sqrt[]{33}}{17}} \end{gathered}$

Second ratio

$\begin{gathered} \theta=K \\ \text{ Adjacent side }=\sqrt[]{33} \\ \text{ Hypotenuse }=17 \\ \cos (\theta)=\frac{\text{ Adjacent side}}{\text{ Hypotenuse}} \\ \boldsymbol{\cos (K)=\frac{\sqrt[]{33}}{17}} \end{gathered}$

Finally, as we can see, sin(J) and cos(K) are equal.