how do you solve arcsin(3/5) without a calculator?
Find an old mathbook with trig tables, go to the sine column, find the nearest value of the angle so that sinØ = .6
The nearest angle you will find is 37°
To solve arcsin(3/5) without a calculator, you can use the properties of trigonometric functions and right triangles.
1. Start by drawing a right triangle. Let one angle be θ, opposite side be 3, and hypotenuse be 5.
2. Use the Pythagorean theorem to find the adjacent side.
a² + b² = c²
a² + 3² = 5²
a² + 9 = 25
a² = 25 - 9
a² = 16
a = √16
a = 4
3. Now you have a right triangle with an opposite side of 3 and an adjacent side of 4.
4. Recall that sinθ = opposite/hypotenuse. In this case, sinθ = 3/5.
5. Since the values of sinθ and opposite/hypotenuse are the same, we have sinθ = 3/5.
6. To find the angle θ, use the inverse sine function or arcsin. This gives us θ = arcsin(3/5).
The final answer is θ = arcsin(3/5).