Pythagorean identities part 1

Pythagorean identities part 1

I can simplify trig expressions.

Warm-up

Multiple Select

ex1) Which one of these is the simplified form of $$\frac{\cos\left(-x\right)}{\sin\left(-x\right)}$$  

• $$\sin^{ }x$$  

• $$\cos^{ }x$$  

• $$\tan^{ }x$$  

• $$-\tan x$$  

• $$-\cot x$$  

Multiple Select

ex2) Which one of these is the simplified form of $$\sin x\left(\sin^2x+\cos^2x\right)$$  

• $$\sin^{ }x$$  

• $$\cos^{ }x$$  

• $$\tan^{ }x$$  

• $$\sin2x$$  

• $$-\cos x$$  

Multiple Select

ex3) Which one of these is the simplified form of $$\cot x\sin x$$  

• $$\sin^{ }x$$  

• $$\cos^{ }x$$  

• $$\tan^{ }x$$  

• $$\sin2x$$  

• $$-\cos x$$  

Multiple Select

ex4) Which one of these is the simplified form of $$\frac{\tan^2x+1}{\sec^3x}$$  

• $$\sin^{ }x$$  

• $$\cos^{ }x$$  

• $$\tan^{ }x$$  

• $$\sec x$$  

• $$-\cos x$$  

Multiple Select

ex5) Which one of these is the simplified form of $$\cos^2x\tan\left(-x\right)$$  

• $$-\cos x\sin x$$  

• $$\cot x\sin x$$  

• $$\tan^{ }x$$  

• $$\sin2x$$  

• $$\cos x\sin x$$  

Multiple Select

ex6) Which one of these is the simplified form of $$\sin\theta-\tan\theta\cos\theta+\cos\left(\frac{\pi}{2}-\theta\right)$$  

• $$\sin\theta$$  

• $$\cos\theta$$  

• $$\tan\theta$$  

• $$-\sin\theta$$  

• 0

But that was a partial list...

This is the full list

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Verify the identity

•  (sin 𝜃 − cos 𝜃)(sin 𝜃 + cos 𝜃) = 1 − 2cos²θ

Verify the identity

Homework

• quizizz