[size=200][b][size=150]Recall the following reciprocal, co-function, even-odd identities as well as the Pythagorean identities.[br][/size][/b][/size][size=150]Whilst you are learning the identities, write the full equation for the identity.[/size][br][br][i][color=#5b0f00][b]Example:[/b][/color][br][br][/i][b]Question:[/b][br] Double angle identity:[br] [math]\sin\left(2x\right)=[/math][br][br][b]Answer:[/b][br] [math]\sin\left(2x\right)=2\sin\left(x\right)\cos\left(x\right)[/math]
What is the pythagorean identity that uses [math]\sin^2\left(x\right)[/math]?
[math]\sin^2\left(x\right)+\cos^2\left(x\right)=1[/math]
Reciprocal identity:[br][math]\frac{1}{\cos\left(x\right)}=[/math]
[math]\frac{1}{\cos\left(x\right)}=\sec\left(x\right)[/math]
Cofunction identity:[br][math]\tan\left(x\right)=[/math]
[math]\tan\left(x\right)=\cot\left(\frac{\pi}{2}-x\right)[/math]
Cofunction identity:[br] [math]\cos\left(x\right)=[/math]
[math]\cos\left(x\right)=\sin\left(\frac{\pi}{2}-x\right)[/math]
Reciprocal identity:[br][math]\frac{1}{\sin\left(x\right)}=[/math]
[math]\frac{1}{\sin\left(x\right)}=\csc\left(x\right)[/math]
Even-odd identity:[br][math]\sec\left(-x\right)=[/math]
[math]\sec\left(-x\right)=\sec\left(x\right)[/math]
Cofunction identity:[br][math]\sin\left(\frac{\pi}{2}-x\right)=[/math]
[math]\sin\left(\frac{\pi}{2}-x\right)=\cos\left(x\right)[/math]
Reciprocal identity:[br][math]\frac{1}{\sec\left(x\right)}=[/math]
[math]\frac{1}{\sec\left(x\right)}=\cos\left(x\right)[/math]
Cofunction identity:[br][math]\sec\left(\frac{\pi}{2}-x\right)=[/math]
[math]\sec\left(\frac{\pi}{2}-x\right)=\csc\left(x\right)[/math]
Even-Odd Identity:[br][math]\sin\left(-x\right)=[/math]
[math]\sin\left(-x\right)=-\sin\left(x\right)[/math]
What is the pythagorean identity that uses [math]\tan^2\left(x\right)[/math]?
[math]\tan^2\left(x\right)+1=\sec^2\left(x\right)[/math]
Even-odd identity:[br][math]\tan\left(-x\right)=[/math]
[math]\tan\left(-x\right)=-\tan\left(x\right)[/math]
Reciprocal identity:[br][math]\frac{1}{\csc\left(x\right)}=[/math]
[math]\frac{1}{\csc\left(x\right)}=\sin\left(x\right)[/math]
Reciprocal identity:[br][math]\cos\left(x\right)=[/math]
[math]\cos\left(x\right)=\frac{1}{\sec\left(x\right)}[/math]
Cofunction identity:[br][math]\cot\left(\frac{\pi}{2}-x\right)=[/math]
[math]\cot\left(\frac{\pi}{x}-x\right)=\tan\left(x\right)[/math]
Reciprocal identity:[br] [math]\cot\left(x\right)=[/math]
[math]\cot\left(x\right)=\frac{1}{\tan\left(x\right)}[/math]
Reciprocal Identity:[br][math]\csc\left(x\right)=[/math]
[math]\csc\left(x\right)=\frac{1}{\sin\left(x\right)}[/math]
Reciprocal identity:[br][math]\frac{1}{\tan\left(x\right)}=[/math]
[math]\frac{1}{\tan\left(x\right)}=\cot\left(x\right)[/math]
Cofunction identity:[br][math]\cot\left(x\right)=[/math]
[math]\cot\left(x\right)=\tan\left(\frac{\pi}{2}-x\right)[/math]
Cofunction identity:[br][math]\sin\left(x\right)=[/math]
[math]\sin\left(x\right)=\cos\left(\frac{\pi}{2}-x\right)[/math]
Reciprocal identity:[br][math]\sec\left(x\right)=[/math]
[math]\sec\left(x\right)=\frac{1}{\cos\left(x\right)}[/math]
What are the three ways one can write the pythagorean identity using trigonometric functions?
[math]\sin^2\left(x\right)+\cos^2\left(x\right)=1[/math][br][math]\tan^2\left(x\right)+1=\sec^2\left(x\right)[/math][br][math]\cot^2\left(x\right)+1=\csc^2\left(x\right)[/math]
Reciprocal identity[br][math]\tan\left(x\right)=[/math]
[math]\tan\left(x\right)=\frac{1}{\cot\left(x\right)}[/math]
Cofunction identity:[br][math]\csc\left(x\right)=[/math]
[math]\csc\left(x\right)=sec\left(\frac{\pi}{2}-x\right)[/math]
Cofunction identity:[br][math]\tan\left(\frac{\pi}{2}-x\right)=[/math]
[math]\tan\left(\frac{\pi}{2}-x\right)=\cot\left(x\right)[/math]
Even-odd identity:[br][math]\cot\left(-x\right)=[/math]
[math]\cot\left(-x\right)=-\cot\left(x\right)[/math]
Reciprocal identity:[br] [math]\frac{1}{\cot\left(x\right)}=[/math]
[math]\frac{1}{\cot\left(x\right)}=\tan\left(x\right)[/math]
Even-Odd Identity:[br][math]-\sin\left(x\right)=[/math]
[math]-\sin\left(x\right)=\sin\left(-x\right)[/math]
Cofunction identity[br][math]\cos\left(\frac{\pi}{2}-x\right)=[/math]
[math]\cos\left(\frac{\pi}{2}-x\right)=\sin\left(x\right)[/math]
Cofunction identity:[br][math]\sec\left(x\right)=[/math]
[math]\sec\left(x\right)=\csc\left(\frac{\pi}{2}-x\right)[/math]
Reciprocal identity:[br][math]\sin\left(x\right)=[/math]
[math]\sin\left(x\right)=\frac{1}{\csc\left(x\right)}[/math]
Cofunction identity:[br][math]\csc\left(\frac{\pi}{2}-x\right)=[/math]
[math]\csc\left(\frac{\pi}{2}-x\right)=\sec\left(x\right)[/math]
Even-odd identity:[br][math]\cos\left(-x\right)=[/math]
[math]\cos\left(-x\right)=\cos\left(x\right)[/math]
What is the pythagorean identity that uses [math]\csc^2\left(x\right)[/math]?
[math]\cot^2\left(x\right)+1=\csc^2\left(x\right)[/math]