What is the Value of Cos 37° in Fraction?

The universally accepted fractional value for $\cos 37^\circ$ is $\frac{4}{5}$. (In decimal form, it is $0.8$).

To understand why the value is $4/5$, you must look at a special right-angled triangle called the '3-4-5 Triangle'.

• If a right-angled triangle has sides of length 3, 4, and a hypotenuse of 5 (which satisfies Pythagoras' theorem $3^2 + 4^2 = 5^2$), the interior angles are perfectly approximately $90^\circ, 53^\circ, \text{and } 37^\circ$.
• In this triangle, the side adjacent to the $37^\circ$ angle has a length of 4.
• The hypotenuse has a length of 5.
• Since $\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, therefore $\cos 37^\circ = \frac{4}{5}$.

Using the same 3-4-5 triangle, you should also memorize these related values:

• $\sin 37^\circ = \frac{3}{5}$ (0.6)
• $\tan 37^\circ = \frac{3}{4}$ (0.75)
• $\cos 53^\circ = \frac{3}{5}$ (0.6)
• $\sin 53^\circ = \frac{4}{5}$ (0.8)