Pre Calc : if θ is an acute angle, solve the equation sin θ = √(3)/2. express your answer in degree?
if θ is an acute angle, solve the equation sin θ = √(3)/2. express your answer in degree
i got 60 degrees becasue sin θ = √(3)/2 = π/3 is that correct? im not sure what acute angle means?
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Yes, there are technically infinitely many solutions to this, but acute specifies the angle is between 0 and 90 degrees (between 0 and π radians), where there is only 1 solution, which is 60 degrees = π/3 radians as you found. See the plot here:
http://www.wolframalpha.com/input/?i=sin+x+%3D+sqr...
This isn't necessary how you need to think about it though since, without a calculator, it won't be clear at all how to find this solution. You should think of a right triangle -- here, take θ as one of the non-right angles, and so sin θ = (opposite side length)/(hypotenuse side length).
So, you have:
opposite side length = sqrt(3)
hypotenuse side length = 2
But this is a special triangle you should think of, which comes up often in class and standardized tests, a 30-60-90 triangle where these numbers are the measures of the angles. In this sort of triangle, the side lengths are x, 2x, sqrt(3)x for some x.
Since we know sqrt(3) and 2 are some side lengths, we can set x = 1, so the side lengths are simply 1, sqrt(3), and 2. Legs are always opposite of the non-90 degree angles, so θ must be either 30 or 60. Since the opposite sqrt(3) is the longer leg (sqrt(3) > 1), θ must be 60 degrees.
An acute angle is one which is less than 90º (or π/2 radians). You're correct. For future reference, an obtuse angle is one which is greater than 90º (or π/2 radians). The obtuse solution to the same question is 2π/3.
√(2)/2 = 0.7071 To get the angle, i exploit the inverse cos button. The inverse cos button is labeled cos-1. The -1 is an exponent. If my calculator in radians, the answer is 0.7854 radian Let me exhibit you the way to transform radians to degrees. The space that an object moves as it travels across the circumference of a circle = 2 * π* r meters. The angle, in radians, that an object rotates because it rotates one revolution = 2 * π radians The angle, in levels, that an object rotates as it rotates one revolution = 360˚ 2 * π radians = 360˚ (2 * π) / 360 = zero.7854 / θ θ = 0.7854 * 360/(2 * π) θ = 45˚ to transform radians to levels, multiply through (360 ÷ 2 * π)