Question

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.

Answer #1

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)

Suppose theta is an acute angle in a right triangle. Given
tan(\theta )=(3)/(5), evaluate:1-sin^(2)(\theta ).

Find the exact value of the expressions cos(a+b), sin(a+b) and
tan(a+b) under the following conditions:
cos(x)=12/13,x lies in quadrant 4, and sin(y)=-4/11, y lies in
quadrant 3
a. cos (a+b) b.sin(a+b) c.tan(a+b)

1.Suppose a = 10 and b = 9.
Find an exact value or give at least two decimal places:
sin(A) =
cos(A) =
tan(A) =
sec(A) =
csc(A) =
cot(A) =
2. Suppose a = 8 and b = 3.
Find an exact value or give at least two decimal places:
sin(A) =
cos(A) =
tan(A) =
sec(A) =
csc(A) =
cot(A) =

- Given cos(x)=-1/12 with 180°<x<270°. Find cos(x/2)
- Given sin(x)= (squareroot 5)/3 where x is an acute angle. Find
sin(x/2)

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...

Evaluate the integral.
pi/2
3
sin2(t) cos(t)
i + 5 sin(t)
cos4(t) j + 4
sin(t) cos(t)
k dt
0

Find the area of one loop of the polar curve r=4*sin(3*theta +
Pi/3)
Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k)
whenever k is an odd integer b) f has a saddle point at (0,k)
whenever k is an even integer) c) f has a local maximum at (0,k)
whenever k is an even integer d) f has a local minimum at (0,k)
whenever k is an odd integer

2)Find the slope of the tangent line to the curve r = sin (O) +
cos (O) at O = pi / 4 (O means theta)
3)Find the unit tangent vector at t = 0 for the curve r (t) =
4sen (t) i + 3tj + cos (t) k
4)A uniform cable measuring 40 feet is hung from the top of a
building. The cable weighs 60 pounds. How much work in foot-pounds
is required to climb 10 feet...

find g'(x)
g(x)= integral (-3/4 + t + cos(Pi/4 (t^2) + t)))
0<x<3

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