Unit circle and triangle trig
Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
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About Unit circle and triangle trig
The unit circle gives the exact sine and cosine of the special angles. Every angle has a reference angle, the acute angle it makes with the x-axis, and its sine and cosine are the reference angle's values with a sign set by the quadrant: cosine is the x value and sine is the y value.
For a triangle that is not a right triangle, the law of sines and the law of cosines take over from SOH-CAH-TOA. Use the law of sines when you know an angle and the side across from it; use the law of cosines when you know two sides and the angle between them, or all three sides.
Keep in mind
- sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2; cos goes the other way round. tan 30° = √3/3, tan 45° = 1, tan 60° = √3.
- Signs by quadrant: sine positive in I and II, cosine positive in I and IV, tangent positive in I and III.
- Radians to degrees: multiply by 180/π. π/6 = 30°, π/4 = 45°, π/3 = 60°.
- Law of sines: a/sin A = b/sin B = c/sin C.
- Law of cosines: c² = a² + b² − 2ab cos C.
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