If sinθ = (square root) 3/2 , find the value of θ in degrees (0 < θ < 90°)
as usual, draw the triangle -- in this case in QI.
sinθ = y/r
cosθ = x/r
Everybody studying trig should know the ratio of sides, and thus the trig ratios, of the 30-60-90° right angled triangles, as well as the 45 -45-90° triangle
for the 30-60-90 the sides are 1 - √3 - 2 units respectively
looking at your sketch of that triangle, notice that
sin 60° = √3/2
if sinØ = √3/2
then Ø = 60° or π/3 radians
sorry. I misread the question.
To find the value of θ in degrees, we need to use the inverse of the sine function, which is called arcsine or sin^(-1).
The arcsine function gives us the angle whose sine is a given value. In this case, we know that sinθ = √3/2.
To find the value of θ, we can use the arcsine function:
θ = sin^(-1)(√3/2)
To evaluate this, you can use a scientific calculator or a trigonometric table.
Using a scientific calculator:
1. Press the inverse sine button (usually labeled as sin^(-1) or arcsin).
2. Enter the value √3/2.
3. Press the equals (=) key.
The result you will get is θ = 60°.
So, the value of θ in degrees is 60°.