Intro to Trig Identitites

Intro to Trigonometric Identities

​You will need to take notes!

The notes and examples you create today will form the foundation of this unit. You will be able to rely on them and return to them in the future.

Note: the videos selected to accompany this activity were created by Brian McLogan. You may see ads before or during the videos. I am not sponsored by and do not promote any of the products/services advertised.

Drag and Drop

$$\sin^2\theta\ +$$ ​

Placeholder

$$=$$ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Drag and Drop

$$1\ +$$ ​ ​ ​

Placeholder

$$=$$ ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Drag and Drop

$$1\ +$$ ​ ​​

Placeholder

​ $$=$$ ​ ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

cotθ=

• cosθ/sinθ

• sinθ/cosθ

• tanθ

• 1/cosθ

Multiple Choice

tanθ=

• cosθ/sinθ

• sinθ/cosθ

• tanθ

• 1/cosθ

Match

Match the following

• 1/csc

• 1/sec

• 1/cot

sin

cos

tan

• sin

• cos

• tan

Match

Match the following

• 1/sin

• 1/cos

• 1/tan

csc

sec

cot

• csc

• sec

• cot

Match

Match the example he provided with the description of the technique.

• $$\frac{x}{y}\cdot\frac{1}{x}=\frac{1}{y}$$

• $$\frac{\left(\frac{x}{y}\right)}{z}=\frac{x}{yz}$$

• $$\tan\theta\cdot\cos\theta=$$ $$\left(\frac{\sin\theta}{\cos\theta}\cdot\cos\theta\right)$$

Look for places where a numerator and denominator will cancel.

Simplify a fraction inside a fration by multiplying by the reciprocal

Replace one or more trig pieces with an identitiy before performing a step

• Look for places where a numerator and denominator will cancel.

• Simplify a fraction inside a fration by multiplying by the reciprocal

• Replace one or more trig pieces with an identitiy before performing a step

Multiple Select

Select the three properties/identities that he mentioned will be used most often.

• Quotient

• Reciprocal

• Pythagorean

• Co-Function

• Even/Odd

Multiple Choice

He demonstrated using a conjugate as a denominator. Here is a similar example. Which of these options is the result after you FOIL these conjugates?

• sinθ

• cot²θ

• tan²θ

• cos²θ

​Time to test these out!

Multiple Choice

Simplify... $$\frac{\tan\left(\Theta\right)}{\sec\left(\Theta\right)}$$  

• $$\sin\left(\Theta\right)$$  

• $$\cos\left(\Theta\right)$$  

Multiple Choice

Simplify (Hint: you will need to FOIL first)

• sinθ

• cot²θ

• tan²θ

• cos²θ

Multiple Choice

 Simplify...  

$$\cos\left(\theta\right)+\sin\left(\theta\right)\tan\left(\theta\right)$$  

• $$\sec\left(\theta\right)$$  

• $$\csc\left(\theta\right)$$  

Multiple Choice

Simplify

• secθ

• cos²θ

• sin²θ

• sin²θ/cos²θ

Multiple Choice

Simplify... $$\frac{\cot\left(\theta\right)\sin\left(\theta\right)}{\cos\left(\theta\right)}$$  

• $$\sec\left(\theta\right)$$  

• 1