Double Angle Formulas

Double Angle Formulas

Open Ended

Use addition formula to find the double angle identity for  $\sin\left(2\alpha\right)$  
In other words, express  $\sin\left(2\alpha\right)$   in terms of  $\sin\alpha$  and  $\cos\left(\alpha\right).$  

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Multiple Choice

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Multiple Select

Use addition identity to prove double angle identity for $\cos\left(2\alpha\right).$  Select all correct answers.

 $\cos\left(2\alpha\right)=?$  

•  $\cos^2\alpha-\sin^2\alpha$  

•  $\sin^2\alpha-\cos^2\alpha$  

•  $2\cos^2\alpha$  

•  $1-2\sin^2\alpha$  

•  $2\cos^2\alpha-1$  

Write down into your notebook.

Write down into your notebook.

Solve highlighted questions in your notebook.

Multiple Choice

• $\frac{24}{25},\frac{7}{25},\frac{24}{7}$

• $\frac{24}{25},\frac{-7}{25},\frac{-24}{7}$

• $\frac{7}{25},\frac{24}{5},\frac{7}{24}$

• $\frac{-7}{25},\frac{24}{25},\frac{-7}{24}$

Multiple Choice

Adv.Math.#22) 

If  $\cos A=\frac{1}{3}$ , where  $\angle A$  is acute, find   $\cos\left(2A\right).$  

• $\frac{-7}{9}$

• $\frac{7}{9}$

• 1

• -1

Multiple Choice

If  $\cos A=\frac{1}{3}$ , where  $\angle A$  is acute, find  $\cos\left(4A\right).$  

•  $\frac{17}{81}$  
  

•  $\frac{-17}{81}$  
  

Open Ended

Find the exact value of $\cos\left(\frac{5\pi}{8}\right)$ . 

Open Ended

Derive a formula for  $\sin\left(4x\right)$  in terms of functions of  $x.$  

Open Ended

Using addition formulas express  $\tan\left(2\alpha\right)$  in terms of  $\tan\left(\alpha\right).$  

Write down into your notebook.