Answer:
Correct answer: second quadrant angle is 3π/4
fourth answer (2√2 + π) / 4
third quadrant angle is 5π/4
first answer (-2√2 + π) / 4
Step-by-step explanation:
Your question does not define the quadrant in which the angle is of the
cos⁻¹ (- √2/2).
If it is in the second quadrant then the angle is 3π/4 and if it is in the third quadrant then the angle is 5π/4
1) second quadrant angle is 3π/4
sin ( cos⁻¹ (- √2/2)) + tan⁻¹ ( sin ( π/2)) = sin ( 3π/4) + tan⁻¹ 1 =
= √2/2 + π/4 = (2√2 + π) / 4
2) third quadrant angle is 5π/4
sin ( cos⁻¹ (- √2/2)) + tan⁻¹ ( sin ( π/2)) = sin ( 5π/4) + tan⁻¹ 1 =
= - √2/2 + π/4 = (-2√2 + π) / 4
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