b) [tex]-\sqrt{3}[/tex] ; d) 0: f) 0; h) [tex]\sqrt{2}[/tex]; j) [tex]-\sqrt{2} /2[/tex]
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b) cot 150°
In the second quadrant, the cosine is negative, and the sine is positive, which makes the cotangent (cos/sin) negative.
- cot 150° = cot (180°-30°) = -cot 30° = [tex]-\sqrt{3}[/tex]
d) cos (7π/2)
This is equivalent to cos (2π + π/2), which is cos (π/2). Cosine is zero at π/2, so,
- cos (7π/2) = cos (π/2) = 0.
f) sin (6π)
Since sine has a period of 2π, sin (6π) is the same as sin (0), which is
h) sec (-7π/4)
This is the reciprocal of the cosine.
cos (-7π/4) is the same as cos (π/4) = [tex]\sqrt{2} /2[/tex], since cosine is even and has a period of 2π.
Therefore,
- sec (-7π/4) = 1/ ([tex]\sqrt{2} /2)[/tex] = [tex]\sqrt{2}[/tex]
j) csc (- 45°)
The cosecant is the reciprocal of the sine.
Since sine is odd, sin (-45°) is -sin (45°), which is [tex]-\sqrt{2} /2[/tex].
Thus,
- csc (- 45°) = [tex]-\sqrt{2} /2[/tex]
