Find the value of sin37°, sin53°, tan37°, tan53° in terms of fraction.

Sin Cos Tan Formula

Assume that ABC is a right triangle with B at its right angle. The following is the formula for sine, cosine, and tangent:

• Sine θ = Opposite side/Hypotenuse = BC/AC
• Cos θ = Adjacent side/Hypotenuse = AB/AC
• Tan θ = Opposite side/Adjacent side = BC/AB

Let’s now consider about the triangle’s sides in terms of the Pythagorean triplet.

Let’s take the right-angled triangle with sides of 3, 4, and 5 cm into consideration.

When the angle = 37° or 53°

• cos A = base / hypotenuse
• So, cos 53° = 3/5
• cos 37° = 4/5

We know that,

• sin 90 – A = cos A
• So cos 53° = sin 37 and cos 37° = sin 53°

Now:

• tan A = perpendicular / base
• tan 37° = 3/4
• tan 53° = 4/3
• sin 37° = 3/5 = cos 53°
• sin 53° = 4/5 = cos 37°
• tan 37° = 3/4 = cot 53°
• tan 53° = 4/3 = cot 37°

Summary:

Find the value of sin37°, sin53°, tan37°, tan53° in terms of fraction.

The value of sin37°, sin53°, tan37°, tan53° in terms of fraction is ⅗, ⅘, ¾ and 4/3. Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles.