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Find the following trigonometric values. Express your answers exactly. cos(225^(@))= ◻ sin(225^(@))= ◻

Find the following trigonometric values.\newlineExpress your answers exactly.\newlinecos⁡(225∘)= \cos \left(225^{\circ}\right)= \newline□ \square \newlinesin⁡(225∘)= \sin \left(225^{\circ}\right)= \newline□ \square

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Find the following trigonometric values.\newlineExpress your answers exactly.\newlinecos⁡(225∘)= \cos \left(225^{\circ}\right)= \newline□ \square \newlinesin⁡(225∘)= \sin \left(225^{\circ}\right)= \newline□ \square
  1. Identify Quadrant: cos⁡(225°)\cos(225°) is in the third quadrant where cosine is negative. Use the reference angle of 45°45°.
  2. Use Reference Angle: cos⁡(225°)=−cos⁡(45°)\cos(225°) = -\cos(45°) because cosine is negative in the third quadrant.
  3. Calculate Cosine: cos⁡(45°)=22\cos(45°) = \frac{\sqrt{2}}{2}. So, cos⁡(225°)=−22\cos(225°) = -\frac{\sqrt{2}}{2}.
  4. Identify Quadrant: sin⁡(225°)\sin(225°) is also in the third quadrant where sine is negative. Use the reference angle of 45°45°.
  5. Use Reference Angle: sin⁡(225°)=−sin⁡(45°)\sin(225°) = -\sin(45°) because sine is negative in the third quadrant.
  6. Calculate Sine: sin⁡(45°)=22\sin(45°) = \frac{\sqrt{2}}{2}. So, sin⁡(225°)=−22\sin(225°) = -\frac{\sqrt{2}}{2}.

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