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Math Problems
Precalculus
Inverses of trigonometric functions
u
⃗
=
(
6
,
7
)
\vec{u}=(6,7)
u
=
(
6
,
7
)
\newline
Find the direction angle of
\newline
u
⃗
\vec{u}
u
. Enter your answer as an angle in degrees between
\newline
0
∘
0^{\circ}
0
∘
and
\newline
36
0
∘
360^{\circ}
36
0
∘
rounded to the nearest hundredth.
\newline
θ
=
□
∘
\theta=\square^{\circ}
θ
=
□
∘
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Convert the angle
\newline
θ
=
133
π
72
\theta=\frac{133\pi}{72}
θ
=
72
133
π
radians to degrees.
\newline
Express your answer exactly.
\newline
θ
=
□
∘
\theta=\square^\circ
θ
=
□
∘
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Which of the following statements are correct for the angle
20
π
3
\frac{20\pi}{3}
3
20
π
radians? (without calculator)
\newline
I. The value of
sec
20
π
3
<
0
\sec \frac{20\pi}{3}<0
sec
3
20
π
<
0
\newline
II. The value of
cosec
20
π
3
<
0
\cosec \frac{20\pi}{3}<0
cosec
3
20
π
<
0
\newline
(A) Only I
\newline
(B) Only II
\newline
(C) Both I and II
\newline
(D) Neither
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If all the angles used in the following statements are in radians, which of the statements are true?
\newline
I.
cos
(
8
π
5
)
>
sin
(
3
π
4
)
\cos(\frac{8\pi}{5}) > \sin(\frac{3\pi}{4})
cos
(
5
8
π
)
>
sin
(
4
3
π
)
\newline
II.
cos
(
8
π
3
)
>
tan
(
2
π
5
)
\cos(\frac{8\pi}{3}) > \tan(\frac{2\pi}{5})
cos
(
3
8
π
)
>
tan
(
5
2
π
)
\newline
(A) Only I
\newline
(B) Only II
\newline
(C) Both I and II
\newline
(D) Neither
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