Find the value of sin 37°, sin 53°, tan 37°, tan 53° in terms of the fraction.

We know from trigonometric identities:

• sin 37° = cos 53°
• sin 53° = cos 37°
• tan θ = sin θ / cos θ

Consider a right triangle with sides 3, 4, 5:

• Opposite side = 3
• Adjacent side = 4
• Hypotenuse = 5

Then the sine and cosine values are:

• sin 37° = opposite / hypotenuse = 3/5
• cos 37° = adjacent / hypotenuse = 4/5
• sin 53° = cos 37° = 4/5
• cos 53° = sin 37° = 3/5

For tangent values:

• tan 37° = sin 37° / cos 37° = (3/5) / (4/5) = 3/4
• tan 53° = sin 53° / cos 53° = (4/5) / (3/5) = 4/3

Final Answer (Fractions)

• sin 37° = 3/5
• sin 53° = 4/5
• tan 37° = 3/4
• tan 53° = 4/3