Question

question 35 (1 point)
which set of primary trigonometric ratios is correct for the angle 225°?
○ a)
○ b)
○ c)
○ d)

Explanation:

Step1: Determine the quadrant of \(225^{\circ}\)

\(180^{\circ}<225^{\circ}<270^{\circ}\), so \(225^{\circ}\) is in the third quadrant. In the third quadrant, \(\sin\theta<0\), \(\cos\theta < 0\), and \(\tan\theta>0\).

Step2: Find the reference angle

The reference angle \(\theta_{r}=225^{\circ}- 180^{\circ}=45^{\circ}\)

Step3: Calculate \(\sin225^{\circ}\)

\(\sin225^{\circ}=-\sin45^{\circ}=-\frac{1}{\sqrt{2}}\) (negative because in the third quadrant)

Step4: Calculate \(\cos225^{\circ}\)

\(\cos225^{\circ}=-\cos45^{\circ}=-\frac{1}{\sqrt{2}}\) (negative because in the third quadrant)

Step5: Calculate \(\tan225^{\circ}\)

\(\tan225^{\circ}=\frac{\sin225^{\circ}}{\cos225^{\circ}}=\frac{-\frac{1}{\sqrt{2}}}{-\frac{1}{\sqrt{2}}}=1\)

Answer:

A. \(\sin225^{\circ}=-\frac{1}{\sqrt{2}},\cos225^{\circ}=-\frac{1}{\sqrt{2}},\tan225^{\circ}=1\)