Question

Find sin(x/2), cos(x/2), and tan(x/2) from the given information.

Sin(x) = 24/25, 0° < x < 90°

Answer #1

(a) Rewrite the expression as an algebraic expression in x
tan(sin-1(x))
(b) Find sin(2x), cos(2x) and tan (2x) from the given
information
csc(x)=4, tan(x)<0

1. Use the given conditions to find the exact value of the
expression.
sin(α) = -5/3, tan(α) > 0, sin(α - 5π/3)
2. Use the given conditions to find the exact value of the
expression.
cos α = 24/25, sin α < 0, cos(α + π/6)
3. Use the given conditions to find the exact value of the
expression.
cot x = √3, cos x < 0, tan(x + π/6)
4. If α and β are acute angles such that...

Find sin x/2, cos x/2 in exact values with the given
information: csc ? = −√26, 180° < ? < 270°.

Find the values of sin x, tan x, cot x, sec x, and csc x and cos
x given that cos(2x)=(3/5) and 3 π /2 < 2x <2 π

use
the squeeze theorum to show that
*** please show work
limx→0 cos(x)x^8 sin(1/x)=0
limx→0 tan(x)x^4 cos(2/x)=0

Find the exact values of sin(θ/2), cos(θ/2), and tan(θ/2) for
the given conditions.
sec θ = −
3
2
; 180° < θ < 270°

9. Suppose that tan(alpha)=3/4 and pi<alpha<3pi/2. Find:
a)sin(2alpha), b)cos(2alpha).
10. Suppose that tan(alpha)=-3 and 3pi/2<alpha<2pi. Find:
a)sin(2alpha), b)cos(2alpha).
16. Given theta is an acute angle with cos(theta)=1/4 , find the
value of tan(theta/2)+tan(2theta). Hint: Find each (using half
angle or double angle formulas) and add them up.

Find the exact values of sin 2θ, cos 2θ, and tan 2θ for the
given value of θ.
cot θ =
4
3
; 180° < θ < 270°

Prove the identity
1) sin(u+v)/cos(u)cos(v)=tan(u)+tan(v)
2) sin(u+v)+sin(u-v)=2sin(u)cos(v)
3) (sin(theta)+cos(theta))^2=1+sin(2theta)

1.Given cos(x) = 1/6 with 3π/2 < x < 2π. Find
the value of cos(2x).
2. which of the following is equivalent to: (8sin(x) +
8 cos(x))^2?
3. which of the following is equivalent to:
12cos(-x)sin(-x)/tan(-x)cot(x+9π)

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