SPreCalc7 6.3.002. 2
Question Description
Hey, I need help with this questions please, they are quite easy, but there are so many of them
.
SPreCalc7 6.3.002.
The sign of a trigonometric function of θ depends on the in/on which the terminal side of the angle lies.In Quadrant II, sin(θ) is .
In Quadrant III, cos(θ) is .
In Quadrant IV, tan(θ) is .
2.
SPreCalc7 6.3.003.
(a) If θ is in standard position, then the reference angle θ
is the acute angle formed by the terminal side of θ and the . So the reference angle for
θ = 110°
is
θ = °,
and that for
θ = 190°
is
θ = °.
(b) If θ is any angle, the value of a trigonometric function of θ is the same, except possibly for sign, as the value of the trigonometric function of
θ.
So
sin(110°) = sin
°
, and
sin(190°) = −sin
°
.
3.
SPreCalc7 6.3.007.
Find the reference angle for the given angle.(a)265°
°
(b)820°
°
(c) −95°
°
4.
SPreCalc7 6.3.011.
Find the reference angle for the given angle.(a)
3π |
5 |
(b)
−0.8π
(c)
0.8
5.
SPreCalc7 6.3.015.
Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)tan(150°)
6.
SPreCalc7 6.3.018.
Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)csc(240°)
7.
SPreCalc7 6.3.025.
Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)sin
3π |
2 |
8.
SPreCalc7 6.3.029.
Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)csc
−
π |
6 |
9.
SPreCalc7 6.3.034.
Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)cos
3π |
4 |
10.
SPreCalc7 6.3.039.
Find the quadrant in which θ lies from the information given.sec(θ) < 0 and tan(θ) < 0
11.
SPreCalc7 6.3.041.
Write the first trigonometric function in terms of the second for θ in the given quadrant.tan(θ), cos(θ); θ in Quadrant III
tan(θ) =
12.
SPreCalc7 6.3.043.
Write the first trigonometric function in terms of the second for θ in the given quadrant.cos(θ), sin(θ); θ in Quadrant IV
cos(θ) =
13.
SPreCalc7 6.3.049.
Find the values of the trigonometric functions of θ from the information given.cos(θ) =
4 |
19 |
, sin(θ) < 0
sin(θ) | = | |
tan(θ) | = |
|
csc(θ) | = |
|
sec(θ) | = |
|
cot(θ) | = |
|
14.
SPreCalc7 6.3.051.
Find the values of the trigonometric functions of θ from the information given.csc(θ) = 4,
θ in Quadrant I
sin(θ) | = |
|
cos(θ) | = |
|
tan(θ) | = |
|
sec(θ) | = |
|
cot(θ) | = |
|
15.
SPreCalc7 6.3.056.
If θ = π/4,
find the value of each expression. (Round your answers to three decimal places, if necessary.)
sin2(θ) | = | |
sin(θ2) | = |
|
16.
SPreCalc7 6.3.058.
Find the area of a triangle with the given description. (Round your answer to one decimal place.)a triangle with sides of length 12 and 23 and included angle 20°
17.
SPreCalc7 6.3.059.MI.
Find the area of the triangle with the given description. (Round your answer to one decimal place.)an equilateral triangle with side of length 14
18.
SPreCalc7 6.3.063.
Find the area of the shaded region in the figure. (Round your answer to two decimal places.)
19.
SPreCalc7 6.3.067.
A graphing calculator is recommended.
A rectangular beam is to be cut from a cylindrical log of diameter d = 22 cm. The figures show different ways this can be done.
(a) Express the cross-sectional area of the beam as a function of the angle θ in the figures.
A(θ) =
(b) Graph the function you found in part (a).
(c) Find the dimensions of the beam with largest cross-sectional area. (Round your answers to two decimal places.)
width | cm |
depth | cm |
20.
SPreCalc7 6.3.068.
The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 20 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle θ in the figures. (Use k as your proportionality constant.)
S(θ) =
If we know the values of sin(x) and cos(x),
we can find the value of
sin(2x)
by using the Formula for Sine.
State the formula:
sin(2x) =
.
2.
SPreCalc7 7.3.002.
If we know the value of cos(x)
x/2
lies, we can find the value of
sin(x/2)
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