Questions: The reciprocal identities state the following. csc (θ) = 1/-- Select -V sec (θ) = 1/□- Select -V cot (θ) = 1/- Select -V

Transcript text: The reciprocal identities state the following. \[ \csc (\theta)=\frac{1}{-- \text { Select }-V} \sec (\theta)=\frac{1}{\square-\text { Select }-V} \quad \cot (\theta)=\frac{1}{- \text { Select }-V} \]

Solution

Solution Steps

Step 1: Identify the reciprocal identities

The reciprocal identities in trigonometry are: \[ \csc(\theta) = \frac{1}{\sin(\theta)}, \quad \sec(\theta) = \frac{1}{\cos(\theta)}, \quad \cot(\theta) = \frac{1}{\tan(\theta)}. \]

Step 2: Fill in the blanks for \(\csc(\theta)\)

The reciprocal of \(\sin(\theta)\) is \(\csc(\theta)\). Therefore: \[ \csc(\theta) = \frac{1}{\sin(\theta)}. \]

Step 3: Fill in the blanks for \(\sec(\theta)\)

The reciprocal of \(\cos(\theta)\) is \(\sec(\theta)\). Therefore: \[ \sec(\theta) = \frac{1}{\cos(\theta)}. \]