Question

Find the angle measure between 0 and 90 degrees that satisfies sin(theta)=1/2

Answer 1

pi/6 radians

Answer 2

or 30 degrees

Answer 3

^^

Answer 4

thanks, but how did you get it? the work is the most important part as we are allowed to use wolfram alpha and all that.

Answer 5

?

Answer 6

its just basic trigonometric angles .You need to learn some basic values for particular angles

Answer 7

yes... pi/6 or 30 degrees are common angles in trig and the sine, cosine and tangent of this (and other common angles) is important to remember...

but as far as the proof that sin(30 degrees) = 1/2, start with a equilateral triangle with a side of 1. can you draw that for me?

Answer 8

In general, you need to do a complicated process to find the sine of an angle
See http://www.homeschoolmath.net/teaching/sine_calculator.php
In the old days, they hired people to work out the answers for each angle and put them in a book of tables.
example http://www.grc.nasa.gov/WWW/k-12/airplane/tablsin.html

However, there are a few angles where the sin of the angle is "easy"
Here are the nice angles, and their sines
angle (in degrees) Sin(angle)
0 0
30 1/2
45 sqrt(2)/2
60 sqrt(3)/2
90 1

People memorize these (and the cosine and tangent)

if you know about 30-60-90 triangles, you can figure out the sin(30º) is 1/2