Download 1.find tan 2x if sin x = 0.5(in sec quad0 tan2x=? In the

1.find tan 2x if sin x = 0.5(in sec quad0
tan2x=?
In the second quadrant, if sin x = ½, then tan x = -1/√3
⎛ 1 ⎞
2
2
2⎜ −
−
−
⎟
⎝
2 tan x
3⎠
3=
3 = ⎛ − 2 ⎞ ⎛ 3⎞ = − 3 = − 3
tan ( 2x ) =
=
⎜⎝
⎟⎜ ⎟
2 =
2
1
2
1− tan x
3⎠ ⎝ 2⎠
3
⎛ 1 ⎞
1−
1− ⎜ −
⎟
3
3
⎝
3⎠
2.simplify the given expression by giving the results in terms of one half of the given
angle.then use the calculator to verify the result.
sqrt 1+cos168 deg=?
1+ cos168 = 2 cos ( 84º )
The value is 0.1478, when rounded to four places.
3.solve the following trig equation analytically(using identities if necessary for exact
values if possible) for values of x for 0<_ x <2pi.
8 tan x + 6 =7(1+ tan x)
8tan x + 6 = 7 + 7tanx
8tanx – 7tanx = 7 – 6
tan x = 1
x = tan-1(1)
x = 45º, and x = 225º
In radians, the solutions are x = π/4 and 5π/4
4.solve the following equation analytically. Use values of x for 0<_ x<2pi.
5 sin x + 5 sin 3x=0
5(sin x + sin 3x) = 0
sin x + sin 3x = 0
sin x + [3 sin x – 4 sin3x] = 0
4 sin x – 4 sin3x = 0
4(sin x)(1 – sin2x) = 0
This means that either sin x = 0, or sin2x = 1.
sin x = 0  x = 0, π
sin2x = 1  x = π/2, 3π/2
Solutions: x = 0, π/2, π, 3π/2
5.use a calculator to evaluate the given expression
sin [tan^-1(-0.2708)] (four decimal places as needed)
sin[tan-1(-0.2708)] = sin[-15.152289] = -0.2614
6.solve for the angle A for the triangle in terms of the given sides. explain you method.
a. A=cos^-1 c/a, because cos A =c/a
b. A=sin^-1 c/a, because sin A=c/a
c. A=cos^-1 a/c, because cos A= a/c
d. A=sin^-1 a/c, because sin A= a/c
The sin of an angle is equal to the length of the side opposite the angle, divided by
the length of the hypotenuse of the right triangle. In the given triangle, the side
opposite angle A has length a, and the hypotenuse has length c. Therefore:
sin A = a/c
This means that A = sin-1(a/c)