Trigonometric Identities and Equations

Trigonometric Identities

Simplifying trigonometric expressions

Proving trigonometric identities

Multiple Choice

Reciprocal Relationships

$$\cot\theta=$$  

• $$-\cot\theta$$  

• $$\frac{1}{\tan\theta}$$  

• $$\frac{1}{\cot\theta}$$  

Multiple Choice

Reciprocal Relationships

$$\csc\theta=$$  

• $$\frac{1}{\sec\theta}$$  

• $$\frac{1}{\cos\theta}$$  

• $$\frac{1}{\sin\theta}$$  

Multiple Choice

Reciprocal Relationships

$$\sec\theta=$$  

• $$\frac{1}{\csc\theta}$$  

• $$\frac{1}{\cos\theta}$$  

• $$\frac{1}{\sin\theta}$$  

Open Ended

Simplify

$$\tan\theta\cdot\cot\theta$$  

Open Ended

Simplify

$$\frac{1}{\sin x\cdot\csc x}$$  

Multiple Choice

• sinx

• cosx

• tanx

• secx

Multiple Choice

$$\sin\left(-\theta\right)=$$  

• $$\sin\theta$$  

• $$-\sin\theta$$  

Multiple Choice

$$\cos\left(-\theta\right)$$  

• $$\cos\theta$$  

• $$-\cos\theta$$  

Multiple Choice

$$\tan\left(-\theta\right)$$  

• $$\tan\theta$$  

• $$-\tan\theta$$  

Evaluate (Write in your notebook and give exact answer where possible):

• sin50°, cos40°

• sin83°,cos7°

• sin30°, cos60°

• tan60°, cot30°

Open Ended

What is the relationship between given pair of angle measures in each question?

Briefly explain why.

function of  $\theta=co$ function of  $co$  mplement of  $\theta$  

Multiple Choice

• sinA

• cosA

• tanA

• secA

Multiple Choice

• $$\sin^2x$$

• $$-\sin^2x$$

• $$\cos^2x$$

• $$-\cos^2x$$

Open Ended

Solve the highlighted questions in the next two slides in your notebook. Show all steps clearly.