Advanced Trigonometry, SMB-014

Determine the quadrant in which the following statement about \(\theta\) is true:

\(\cos \theta\) is negative and \(\sin \theta\) is negative. (1 mark)

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\(\tan \theta\) is negative and \(\cos \theta\) is positive. (1 mark)

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a. \(\text{3rd quadrant}\)

b. \(\text{4th quadrant}\)

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a. \(\cos \theta \ \Rightarrow\ \text{–ve in 2nd/3rd quadrant}\)

\(\sin \theta \ \Rightarrow\ \text{–ve in 3rd/4th quadrant}\)

\(\Rightarrow\ \text{3rd quadrant}\)

b. \(\tan \theta \ \Rightarrow\ \text{–ve in 2nd/4th quadrant}\)

\(\cos \theta \ \Rightarrow\ \text{+ve in 1st/4th quadrant}\)

\(\Rightarrow\ \text{4th quadrant}\)