Trigonometry

• To find a missing side of triangle ABC, a = root (b^2 + c^2 - 2 b c cos A).
• To find a missing angle of triangle ABC, cos A = (b^2 + c^2 - a^2)/2 b c.
• The sine rule for triangle ABC is a/sin A = b/sin B = c/sin C.
• The area of a triangle ABC is 1/2 a b sin C.
• 1 radian = 180 degrees/ pi.
• The arc length of a sector of a circle is l = r $\theta$ .
• The area of a sector of a circle is A = 1/2 r^2 $\theta$ .
• The area of a segment (area between a chord and outside of the circle) is A = 1/2 r^2 ( $\theta$ - sin $\theta$ ).
• When $\theta$ is close to zero, sin $\theta$ is approximately equal to $\theta$, cos $\theta$ is 1 - ($\theta$ ^2 /2) and tan $\theta$ is $\theta$ .
• sec ^2 x = tan ^2 x + 1.
• cosec ^2 x = cot ^2 x + 1.
• When y = sin x, x = arcsin y, and the same for cos and tan.
• Sin 2x = 2 sin x cos x.
• Cos 2x = cos ^2 x - sin ^2 x = 1 - 2 sin ^2 x = 2 cos ^2 x -1.
• Tan 2x = 2 tan x/1 - tan ^2 x.
• +/- a sin x +/- b cos x can be simplified to either R sin (x +/- $\theta$ ) or R cos (x +/- $\theta$ ). Use sin when the coefficient of sin is positive and cos when the coefficient of cos is positive.