Trigonometric Identities

Which of the following is NOT a valid trigonometric identity?

• $\csc\theta=\frac{\sec\theta}{\tan\theta}$
  

• $\csc\theta=\frac{1}{\cos\theta}$
  

• $\csc\theta=\cot\theta\cdot\sec\theta$
  

• $\csc\theta=\sec\left(90\degree-\theta\right)$
  

Which of the following is NOT a valid trigonometric identity

• $1\ =\cos\theta\cdot\sec\theta$

• $1\ =\ \sin^2\theta+\cos^2\theta$

• $1\ =\ \tan\theta\cdot\cot\theta$

• $1=\csc^2\theta+\cot^2\theta$

Tags

CCSS.HSF.TF.C.8

Mark the box on all the wrong reciprocals

• $\tan\theta=\frac{1}{\cot\theta}$

• $\sin\theta=\frac{1}{\sec\theta}$

• $\cos\theta=\frac{1}{\csc\theta}$

• $\cot\theta=\frac{1}{\sin\theta}$

• $\csc\theta=\frac{1}{\cot\theta}$

The equation

 $\sin^2\theta+\cos^2\theta=1$  is an example of what kind of trigonometric identity? (One word answer only)

(a)  

Explain the meaning of SOHCAHTOA in 3 sentences

Express the following in terms of sine only: $\cos\theta\cdot\csc\theta\cdot\cot\theta$  

Express in terms of cotangent only: $\frac{1-\tan\theta}{1+\tan\theta}$  

Express in terms of sine only: $\frac{\cos\theta}{\sec\theta+\tan\theta}$  

Prove that: $\frac{1+\cos\theta}{\cos\theta}=1+\sec\theta$  

Prove that: $\cos\theta+\tan\theta\cdot\sin\theta=\sec\theta$