1-6 Solve using Pythagorean identities

Simplify:  $\sec^2\theta-\tan^2\theta$  

• 1

• -1

•  $\csc\theta$  

•  $-\csc\theta$  

Which of the following is not a pythagorean identity?

•  $\cot^2x+1=\csc^2x$  

•  $\cot^2x-\csc^2x=-1$  

•  $\csc^2x-\cot^2x=1$  

•  $\csc^2x+1=\cot^2x$  

Given sin⊖ =  $\frac{-1}{3}$   and cos⊖ =  $\frac{2\sqrt{2}}{3}$  , find the exact value for tan⊖.

•  $-2\sqrt{2}$  

•  $\frac{\sqrt{2}}{4}$  

•  $-3$  

•  $\frac{-\sqrt{2}}{4}$  

Given cos ⊖ =  $\frac{\sqrt{3}}{5}$   and tan⊖ < 0 , find the exact value for sin⊖ using pythagorean identities.

•  $\frac{5\sqrt{3}}{3}$  

•  $\frac{\sqrt{22}}{5}$  

•  $\frac{22}{25}$  

•  $\frac{-\sqrt{22}}{5}$   

Which expression always equals 1?

• $\cos^2\theta-\sin^2\theta$

• $\cot^2\theta+\csc^2\theta$

• $\tan^2\theta+\sec^2\theta$

• $\cos^2\theta+\sin^2\theta$

The expression  $\sin^2x+\cos^2x-b^2$  is equal to

• 1

•  $b^2$  

•  $\left(1+b\right)\left(1-b\right)$  

•  $\sin x\cos x-b$  

If  $\cos\theta=-\frac{4}{5}$  and  $\theta$  lies in Quadrant II, what is the value of  $\tan\theta$  ?

•  $-\frac{3}{4}$  

•  $-\frac{4}{3}$  

•  $\frac{3}{4}$  

•  $\frac{4}{3}$  

If x is a positive acute angle and  $\cos x=\frac{\sqrt{3}}{4}$  , what is the exact value of  $\sin x$  ?

•  $\frac{1}{2}$  

•  $\frac{4\sqrt{13}}{13}$  

•  $\frac{\sqrt{13}}{4}$  

•  $-\frac{1}{2}$  

Which of the following is NOT a Pythagorean identity?

• $\tan^2x+1=\sec^2x$

• $\cos2x\ =\ \cos^2x-\sin^2x$

• $\sin^2x\ +\ \cos^2x=1$

• $1+\cot^2x\ =\ \csc^2x$

Pythagorean:  $\sin^2x-1=?$  

•  $-\cos^2x$ 

•  $\cos^2x$ 

•  $\cos^2x-1$ 

•  $1-\cos^2x$