[size=150][size=200][size=100]This is an introduction to the main trigonometric functions of [b][color=#38761d]sine[/color][/b], [b][color=#9900ff]cosine[/color][/b], and [b][color=#ff7700]tangent[/color][/b].[br][br][b][color=#38761d]Sine[/color][/b], [b][color=#9900ff]cosine[/color][/b], and [b][color=#ff7700]tangent[/color][/b] are commonly abbreviated as '[b][color=#38761d]sin[/color][/b]', '[b][color=#9900ff]cos[/color][/b]', and '[b][color=#ff7700]tan[/color][/b]'.[br][br]The [b][color=#ff00ff]input[/color][/b] of a trigonometric function is an [b][color=#ff00ff]angle measure[/color][/b] (labeled as [b][color=#ff00ff]θ[/color][/b] below).[/size][/size][/size]
[b][color=#45818e][u]Move[/u] the[/color] [color=#666666][u]right angle vertex[/u][/color] [color=#45818e]and the [/color][color=#ff00ff][u]slider[/u][/color][color=#45818e] to [u]change[/u] the [u]size[/u] and [u]shape[/u] of the triangle[/color][color=#1e84cc].[br][br][/color][color=#45818e]Observe what happens to the values.[/color][/b]
How do the trig functions relate to the ratios of the sides?
The outputs of the trig functions are ratios of the sides of the triangle.
[size=150][b][color=#38761d]S[/color][color=#bf9000]O[/color][color=#0000ff]H[/color][color=#9900ff]C[/color][color=#ff0000]A[/color][color=#0000ff]H[/color][color=#ff7700]T[/color][color=#bf9000]O[/color][color=#ff0000]A[/color][/b] is a mnemonic device used in Trigonometry to help us remember the functions.[br][br]What does it stand for? [br][i]Hint: How does it relate to the above ratios?[/i][/size]
[color=#38761d][b]S[/b]in(θ)[/color] = [color=#bf9000][b]O[/b]pposite[/color]/[color=#0000ff][b]H[/b]ypotenuse[/color] ([b][color=#38761d]S[/color][color=#bf9000]O[/color][color=#0000ff]H[/color][/b])[br][br][color=#9900ff][b]C[/b]os(θ)[/color] = [color=#ff0000][b]A[/b]djacent[/color]/[color=#0000ff][b]H[/b]ypotenuse[/color] ([b][color=#9900ff]C[/color][color=#ff0000]A[/color][color=#0000ff]H[/color][/b])[br][br][color=#ff7700][b]T[/b]an(θ)[/color] = [color=#bf9000][b]O[/b]pposite[/color]/[color=#ff0000][b]A[/b]djacent[/color] ([b][color=#ff7700]T[/color][color=#bf9000]O[/color][color=#ff0000]A[/color][/b])
[size=200][b][size=100][size=150][color=#45818e]Make note of SOHCAHTOA for future reference.[/color][/size][/size][/b][/size]