Find the values of sin 37°, sin 53°, tan 37°, and tan 53° in terms of fractions.

Solution

Given

We are required to find the values of:

• sin 37°
• sin 53°
• tan 37°
• tan 53°

Step 1: Consider a Right-Angled Triangle

Let us consider a right-angled triangle △ABC right-angled at B.

• ∠A = 37°
• ∠C = 53°
• Since 37° + 53° = 90°

Step 2: Assume Sides of the Triangle

Take the sides of the triangle in the ratio:

• AB = 3 units (opposite to 37°)
• BC = 4 units (adjacent to 37°)
• AC = 5 units (hypotenuse)

Step 3: Find Required Trigonometric Ratios

For angle 37°:

For angle 53°:

Final Answer