HPC Section 5.1 Part 2

PreCalculus Section 5.1

Using Fundamental Identities

Part 2

Multiple Choice

$$\sin^2\theta+\cos^2\theta=1$$  can be derived from  $$x^2+y^2=r^2$$  by dividing the equation by. . . 

• $$r^2$$  

• $$y^2$$  

• $$x^2$$  

• $$\theta^2$$  

Multiple Select

$$\sin^2\theta+\cos^2\theta=1$$  

Choose the equivalent equations.

• $$\sin^2\theta=1-\cos^2\theta$$  

• $$\cos^2\theta=1-\sin^2\theta$$  

• $$\sin\theta=1-\cos\theta$$  

• $$\cos\theta=1-\sin\theta$$  

• $$\sin\theta=\sqrt[]{1-\cos^2\theta}$$

Multiple Select

$$\cot^2\theta+1=\csc^2\theta$$  

Choose the equivalent equations?

• $$\cot^2\theta=\csc^2\theta-1$$  

• $$\cot^2\theta-\csc^2\theta=1$$  

• $$\csc^2\theta-\cot^2\theta=1$$  

• $$\cot\theta=\sqrt{\csc^2\theta-1}$$  

• $$\csc\theta=1+\cot\theta$$  

Multiple Choice

$$\sec x\cos x$$

Use the identities to simplify

• 1

• $$\cos^2x$$  

• $$\sec^2x$$  

• None of these
  

Multiple Select

$$\tan x\csc x$$

Use the identities to simplify

• $$\frac{1}{\cos x}$$  

• $$\sec x$$  

• $$\frac{\sin x}{\cos^2x}$$  

• 1
  

Multiple Select

$$\left(1\ -\ \cos^2x\right)\left(\csc x\right)$$

Use the identities to simplify

• $$\tan x\sin x$$  

• $$\sin x$$  

• $$1\ -\ \tan x$$  

• 1
  

Open Ended

$$\left(\sec x\ -\ \tan x\right)\left(\sec x+\tan x\right)$$  Simplify.

Day 2
Page 354 – 355 # 10, 19, 27 – 31 , 34, 36, 40, 45 – 51 odd, 55, 57, 59,  79​

Homework

Pg 354 - 355