Derivatives: using trigonometric identities

Multiple Choice

What is equal to $$\frac{1}{\sec\ \theta}$$  ?

• Nothing

• $$\cos\ \theta$$  

• $$\frac{1}{\cos\ \theta}$$  

• 1

Multiple Choice

What is the derivative of $$g\left(\theta\right)=\sin\theta+\cos\theta$$  ?

• $$0$$  

• $$\cos\theta-\sin\theta$$  

• $$\cos\theta+\sin\theta$$  

• $$2\cos\theta$$  

Multiple Choice

What is equal to $$\frac{\sin^2x}{\cos^2x}$$  ?

• Nothing

• $$\tan x$$  

• $$\tan^2x$$  

• 1

Multiple Choice

What is the derivative of $$f\left(x\right)=\tan\ x$$  ?

• $$0$$  

• $$\sec\ x$$  

• $$\sec^2\ x$$  

• $$1$$  

Multiple Choice

What is the derivative of $$\cos\left(8x^3\right)$$  ?

• $$-\sin\left(8x^3\right)$$  

• $$-24x^2\sin\left(8x^3\right)$$  

• $$-3x^2\sin\left(8x^3\right)$$  

• $$\sin\left(8x^3\right)$$  

Multiple Choice

What is equal to $$\sec^2\ x$$  ?

• Nothing

• $$\cos^2\ x$$  

• $$\frac{1}{\cos^2\ x}$$  

• $$\frac{1}{\cos\ x}$$  

Fill in the Blanks

What is the derivative of 1?

​SUMMARY

When should you try to use the trigonometric identities before finding the derivative:

​

1. * The trigonometric function is in the denominator​

2. ​

3. * There's two or more different trigonometric functions with the same angle

​We're done! See you tomorrow! :)