Monday, September 12, 2011

The "famous" trig values between 0 and 90 degrees inclusive


sin 0° = 0
cos 0° = 1
tan 0° = sin0°/cos0° = 0

30°
sin 30° = ½
cos 30° = sqrt(3)/2
tan 30° = sin 30°/cos 30° =sqrt(3)/3

45°
sin 45° =sqrt(2)/2
cos 45° =sqrt(2)/2
tan 45° = sin 45°/cos 45° =1

60°
sin 60° =sqrt(3)/2
cos 60° = ½
tan 60° = sin 60°/cos 60° =sqrt(3)

90°
sin 90° =1
cos 90° =0
tan 90° = sin 90°/cos 90° = UNDEFINED (can't divide by zero)

In the first quadrant, we have these three situations.

As the angle increases, sine increases, from a low of 0 to a high of 1.

As the angle increases, cosine decreases, from a high of 1 to a low of 0.

As the angle increases, tangent increases, from a low of 0 to a high of infinity.


A little preview of coming attractions.  We are not always going to think of sine and cosine as values on the Normal Standard Position Right Triangle, but instead as the x and y values on the unit circle, defined by the formula x² + y² = 1.

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