Trigonometry: Sine, Cosine, Tangent

The sine formula is $\sin (\theta )=\frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is $3\text{ cm}$ and the hypotenuse is $5\text{ cm}$. So, the sine of the angle is $\frac{3}{5}$.

The cosine formula is $\cos (\theta )=\frac{\text{Adjacent}}{\text{Hypotenuse}}$. Here, the adjacent side is $8\text{ cm}$ and the hypotenuse is $10\text{ cm}$. So, the cosine of the angle is $\frac{8}{10}=\frac{4}{5}$.

The sine formula is $\sin (\theta )=\frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is $8\text{ cm}$ and the hypotenuse is $16\text{ cm}$. So, the sine of the angle is $\frac{8}{16}=\frac{1}{2}$.

Using the tangent formula $\tan (\theta )=\frac{\text{Opposite}}{\text{Adjacent}}$, here the opposite side is $5\text{ cm}$ and the adjacent side is $12\text{ cm}$. So, the tangent of the angle is $\frac{5}{12}$.

Using the cosine formula $\cos (\theta )=\frac{\text{Adjacent}}{\text{Hypotenuse}}$, here the adjacent side is $12\text{ cm}$ and the hypotenuse is $13\text{ cm}$. So, the cosine of the angle is $\frac{12}{13}$.

The sine formula is $\sin (\theta )=\frac{\text{Opposite}}{\text{Hypotenuse}}$. Here, the opposite side is $8\text{ cm}$ and the hypotenuse is $16\text{ cm}$, so $\sin (\theta )=\frac{1}{2}$. Using the inverse sine function, $\theta ={\sin }^{-1}\left(\frac{1}{2}\right)=30^{\circ }$.