cosine (theta) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction , and StartFraction 3 pi Over 2 EndFraction less-than thet
a less-than 2 pi, evaluation sine (theta) and tangent (theta)
2 answers:
9514 1404 393
Answer:
sin(θ) = -√2/2
tan(θ) = -1
Step-by-step explanation:
The reference angle is arccos(√2/2) = 45°. The sine has the same magnitude, so the tangent (ratio of sine to cosine) has a magnitude of 1.
The angle is given as a 4th-quadrant angle. Both the sine and tangent are negative in the 4th quadrant.
sin(θ) = -√2/2
tan(θ) = -1
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In the attachment, the angle of interest is 315° (7π/4). The given unit-circle coordinates are ...
(x, y) = (cos(θ), sin(θ))
tan(θ) = y/x
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