Determine an expression using trigonometric ratios of special angles that simplifies to an answer of sqrt3/2. Use three different angles.
sin 60° = √3/2
cos 30° = √3/2
sin 120° = √3/2
sin 60
cos 30
sin 120
(all degrees, not radians)
Oh wow, we got the same answer reiny cool
They were the most obvious ones.
I guess so
To determine an expression using trigonometric ratios of special angles that simplifies to an answer of √3/2, we need to consider the special angles of 30°, 45°, and 60°.
1. For the angle of 30°:
The trigonometric ratios for 30° are as follows:
sin(30°) = 1/2
cos(30°) = √3/2
tan(30°) = 1/√3
To get √3/2 as the answer, we can use the cosine function:
cos(60°) = √3/2
2. For the angle of 45°:
The trigonometric ratios for 45° are as follows:
sin(45°) = √2/2
cos(45°) = √2/2
tan(45°) = 1
To get √3/2 as the answer, we can use the sine function:
sin(60°) = √3/2
3. For the angle of 60°:
The trigonometric ratios for 60° are as follows:
sin(60°) = √3/2
cos(60°) = 1/2
tan(60°) = √3
In this case, we already have the desired expression.
Therefore, the expressions using trigonometric ratios of special angles that simplify to an answer of √3/2 are:
cos(60°)
sin(60°)
sin(45°)