Trig Identities and Solving Trig Equations

Which of these are equal to 1? (Check all that apply)

• sin²(θ) + cos²(θ)

• sec²(θ) - tan²(θ)

• csc²(θ) - cot²(θ)

• tan²(θ) - cos²(θ)

Which of these is false?

•  $\cos\left(\frac{\pi}{2}-\theta\right)=\sin\left(\theta\right)$  

•  $\sin\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$  

•  $\sec\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$  

•  $\tan\left(\frac{\pi}{2}-\theta\right)=\cot\left(\theta\right)$  

Each trig function has a "cofunction" (Ex: sine and cosine are cofunctions).

How are cofunctions related to each other? (Check all that apply)

• Cofunctions of complementary angles are equal.

• Cofunctions are reciprocals of each other.

• Cofunctions are inverses of each other.

• Cofunctions are negatives of each other.

 $\frac{\tan\left(\theta\right)}{\cot\left(\theta\right)}\equiv$  

•  $1$  

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

•  $\tan^2\left(\theta\right)$  

•  $\sec^2\left(\theta\right)$  

• x = 0

Find $\sin\theta$  if  $\cos\theta=\frac{3}{5}$  .

•  $0.80$  

•  $0.63$  

•  $1.25$  

•  $1.58$  

Find $\sin\theta$  if  $\tan\theta=12$  .

•  $1.003$  

•  $0.997$  

•  $1.041$  

•  $0.961$  

If $\tan\theta=\frac{8}{4}$   , find  $\cos\theta$  .

•  $2.24$  

•  $0.45$  

•  $1.73$  

•  $0.58$  

If $\tan\theta=\frac{5}{3}$   , find  $\sec\theta$  .

•  $0.65$  

•  $1.63$  

•  $1.94$  

•  $0.94$  

If $\sec\theta=-2$ , find $\cos\theta$ .

• $-\frac{1}{2}$

• $\frac{1}{2}$

• $2$

• $-\frac{1}{4}$