Question

1. Find all angles
θ,0≤θ≤2π

(Double angle
formula, To two decimal places)

a) Tan theta
= 0.3, b) cos theta = 0.1, c) sin theta = 0.1,

d) sec theta
= 3

Answer #1

Angle θ is an angle in the fourth quadrant and cos(θ)=1/3. Find
tan(θ)?

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.

1. Let θ < 0 be an angle in standard position. (a) Choose a
value for θ (in radians) and graph θ. (b) Find the reference angle
of θ. (c) Find numbers 0 < x < 2π and n ∈ Z so that θ = x +
2πn. (d) Convert θ into degrees.
2. Let θ1 and θ2 be coterminal angles in
standard position. (a) Choose a value for θ1 and
θ2 (in radians) and graph both angles. (b) Find...

Find all angles θ between 0° and 180° satisfying the given
equation. Round your answer to one decimal place. (Enter your
answers as a comma-separated list.)
sin(theta)=3/4

Find all theta from (-pi,pi) for which the tangent line of
r=tan(theta/2) is horizontal.
I have gotten to
1/2sec^2(theta/2)*sin(theta)+tan(theta/2)*cos(theta)=0
How do I solve for 0?

Use the cofunction identities to find an angle theta
that makes the statement true.
1) sin( 3theta - 17degrees)=cos (theta+43degrees)
2) cot 5theta= tan 4theta
Use identities to write the expression as a single
function of x or theta.
1) cos (theta - pi)
Verify that the equation is an identity.
1) sin (x+y)-sin(x-y)=2 cos x sin y

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

For the following exercises, find all exact solutions on [0,
2π)
23. sec(x)sin(x) − 2sin(x) = 0
25. 2cos^2 t + cos(t) = 1
31. 8sin^2 (x) + 6sin(x) + 1 = 0
32. 2cos(π/5 θ) = √3

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)

Using MATLAB
The range of an object shot at an angle θ (with respect to
x-axis), with the initial velocity of V0 (in the absence of air
resistance), is calculated by the following formula:
range=(Vo^2/g)(sin(2theta)) where (0<=theta<=pi/2) And the
trajectory of object is given by:
h=tan(theta).x-(g/2Vo^2*cos^2(theta)).x^2 .Where h is the height of
the object at each x location and g = 9.81 m/s2.
a) Using π/8 increment size for the angle and V0 = 10 m/s, plot
the trajectories of...

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