Question

Prove the following

(4 sin(θ) cos(θ))(1 − 2 sin2 (θ)) = sin(4θ)

cos(2θ) /1 + sin(2θ) = cot(θ) − 1/ cot(θ) + 1

cos(u) /1 + sin(u) + 1 + sin(u) /cos(u) = 2 sec(u)

Answer #1

Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ}
of F[0, 2π]

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)

Name the Quadrant
1. cot q = -3 , tan q =
2. cot q = -3 , tan q =
3. sec q = 1.5 , cos q =
4. cos q = -3/5 , sec q =
Solve the identity function
1. tan x / sin x
2. cos t / cot t
3. cos a csc a tan a
4. cot t sec t sin t
5. 1 - cos2 q
6. csc2 q - 1
7....

3. Let P = (a cos θ, b sin θ), where θ is not a multiple of π/2
be a point on the ellipse (x 2/ a2 )+ (y 2/ b 2) = 1, where a ≥ b
> 0; and let P1 = (a cos θ, a sin θ) the corresponding on the
circle x 2 /a2 + y 2/ a2 = 1. Prove that the tangent to the ellipse
at P and the tangent to the circle at...

Find the critical numbers of the function.
18 cos(θ) + 9 sin2(θ)

1. Given cos 2θ = −5/18 and 180<θ<270, find values of sinθ
and cosθ
2. Given the exact value of cos(2 arctan 4/3)
3. Solve 2cosθ = 2cos2θ for all exact solutions in degrees

3.5.2a. If csc(θ)=3 and (π/2) <?θ< ?π ( signs are less
than and equal to) find the
following and give exact answers:
(a.) sin(θ)
(b.) cos(θ)
(c.) tan(θ)
(d.) sec(θ)
(e.) cot(θ)

Find the area of the region inside the circle r = sin θ but
outside the cardioid r = 1 – cos θ. Hint, use an identity for cos
2θ.

Find f. f ''(θ) = sin(θ) + cos(θ), f(0) = 5, f '(0) = 4

Find f.
f ''(θ) = sin(θ) +
cos(θ), f(0) =
4, f '(0) = 3
f(θ) =

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