Trig Review - Identities & Sum/Difference Formulas

From the given list, select all equivalent forms of the Pythagorean Identity

 $\cos^2\theta+\sin^2\theta=1$  

•  $1+\tan^2\theta=\sec^2\theta$  

•  $1+\cot^2\theta=\sec^2\theta$  

•  $1+\tan^2\theta=\csc^2\theta$  

•  $1+\cot^2\theta=\csc^2\theta$  

Select all correct even/odd identities from the given list.

•  $\sin\left(-x\right)=\sin\left(x\right)$  

•  $\cos\left(-x\right)=\cos\left(x\right)$  

•  $\tan\left(-x\right)=-\tan\left(x\right)$  

•  $\sin\left(-x\right)=-\sin\left(x\right)$  

•  $\cos\left(-x\right)=-\cos\left(x\right)$  

Tags

CCSS.HSF.TF.A.4

From the given list, select all equivalent forms of the Pythagorean Identity

$\cos^2\theta+\sin^2\theta=1$

• $\sin^2\theta=\cos^2\theta-1$

• $\cos^2\theta=1-\sin^2\theta$

• $\cos^2\theta=1+\sin^2\theta$

• $\sin^2\theta=1-\cos^2\theta$

Tags

CCSS.HSF.TF.C.8

What is the best first step for proving  $\frac{1}{1+\cos x}=\frac{1-\cos x}{\sin^2x}$  ?

• Multiply the numerator and denominator by the conjugate  $\left(1-\cos x\right)$  

• Square the numerator and denominator

• Use a Pythagorean Identity for the denominator to change the  $\left(1+\cos x\right)$  to  $\left(\sin^2x\ +\cos^2x+\cos x\right)$  

• Split up the denominator

Which of the following is the best first step to verify the identity

 $\cos^4x-\sin^4x=2\cos^2x-1$  

• Split up the  $\left(\sin^4x\right)$  as  $\left(\sin^2x\right)\left(\sin^2x\right)$  to set up a Pythagorean Identity substitution 

• Split up the  $\left(\cos^4x\right)$  as  $\left(\cos^2x\right)\left(\cos^2x\right)$  to set up a Pythagorean Identity substitution 

• Factor the left side using the difference of squares

• Use a Pythagorean Identity on the right side to change  $\left(2\cos^2x-1\right)$  to  $\left(2\left(1-\sin^2x\right)-1\right)$  

Find the exact value of

 $\cos105\degree$  

•  $\frac{\sqrt{2}+\sqrt{6}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{3}}{2}$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

Tags

CCSS.HSF.TF.C.9

Write the following as a single trigonometric expression, then evaluate the expression.

 $\sin37\degree\cos113\degree+\cos37\degree\sin113\degree$  

•  $\sin150\degree=\frac{\sqrt{3}}{2}$  

•  $\sin150\degree=\frac{1}{2}$  

•  $\sin\left(-76\degree\right)\approx-0.9703$  

•  $\sin\left(-76\degree\right)\approx0.2419$  

Tags

CCSS.HSF.TF.C.9

If $\cos A=\frac{3}{5}$  where  $0\degree\le A\le90\degree$  and  $\sin B=\frac{5}{13}$ where  $90\degree\le B\le180\degree$  find  $\cos\left(A+B\right)$   .

(a)  

Tags

CCSS.HSF.TF.C.9