Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.
- $\rhd$ Proof of the Pythagorean trig identity (6:12) Proof of $\sin^2\theta+\cos^x\theta=1$
- $\rhd$ Verifying Trigonometric Identities (24:50) Verify identities such as $\sin x\sec x =\tan x$, and $\tan^2(x)\cot^2(x)=1$, and $\cot x\sec x\sin x=1$, and $\sin x \tan x=\frac{1-\cos^2 x}{\cos x}$, and $\sin x \tan x+\cos x=\sec x$, and $\sec x-\cos x=\tan x\sin x$.
- $\rhd$ Using the Pythagorean trig identity (6:15) Given that $\sin(\theta)=\frac 1 2$ and that $\theta$ is in the third quadrant, find $\tan(\theta)$.
- * Practice: Use the Pythagorean identity to solve problems of the type: given that $\theta$ is in the third quadrant and that $\cos(\theta) = \frac{-12}{13}$, find $\sin(\theta)$.
- $\rhd$ Angle addition formulas (11:06) Formulas for $\sin(a\pm b)$, $\cos(a\pm b)$, $\cos(2a)$, $\sin(2a)$.
- $\rhd$ Using the cosine angle addition formula (5:13) Given a right triangle $\Delta ABC$ and the lengths of its sides, find the cosine of $\angle ABC+60^o$.
- $\rhd$ Using the cosine double-angle formula (3:27) Given a right triangle $\Delta ABC$ and the lengths of its sides, find the cosine of $2\cdot\angle ABC$.
